To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope of a line passing through the points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Substitute the points (0, -4) and (1, -1) into the formula:
m = (-1 - (-4)) / (1 - 0) = 3 / 1 = 3
Next, we know that the y-intercept of the line is -4. Therefore, the equation of the line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept. Substituting the slope m = 3 and the y-intercept b = -4 into the equation, we have:
y = 3x - 4
So, the equation of the line in slope-intercept form is y = 3x - 4.
Use the image to answer the question.An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.Using the graph, derive the equation of the line in slope-intercept form.(1 point)
13 answers
Use the image to answer the question.An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.Write the equation of the line in slope-intercept form.(1 point)
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope of a line passing through the points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Substitute the points (0, 1) and (1, -4) into the formula:
m = (-4 - 1) / (1 - 0) = -5 / 1 = -5
Next, we know that the y-intercept of the line is 1. Therefore, the equation of the line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept. Substituting the slope m = -5 and the y-intercept b = 1 into the equation, we have:
y = -5x + 1
So, the equation of the line in slope-intercept form is y = -5x + 1.
m = (y2 - y1) / (x2 - x1)
Substitute the points (0, 1) and (1, -4) into the formula:
m = (-4 - 1) / (1 - 0) = -5 / 1 = -5
Next, we know that the y-intercept of the line is 1. Therefore, the equation of the line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept. Substituting the slope m = -5 and the y-intercept b = 1 into the equation, we have:
y = -5x + 1
So, the equation of the line in slope-intercept form is y = -5x + 1.
Use the image to answer the question. A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis. Is this the correct graph of y=−1/3x+4?(1 point)
To determine if the line on the graph matches the equation y = -1/3x + 4, we can compare the slope and the y-intercept of the equation with the plotted line on the graph.
The equation y = -1/3x + 4 is in slope-intercept form, where the slope is -1/3 and the y-intercept is 4.
Looking at the plotted points (0, 3) and (3, 2), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (3 - 0)
m = -1 / 3
The calculated slope is -1/3, which matches the slope in the equation y = -1/3x + 4.
Now, let's compare the y-intercept. The y-intercept of the equation is 4, which means the line should pass through the point (0, 4). However, the plotted line passes through the point (0, 3) instead of (0, 4).
Therefore, based on the y-intercept not matching, the plotted line on the graph is not the correct graph of y = -1/3x + 4.
The equation y = -1/3x + 4 is in slope-intercept form, where the slope is -1/3 and the y-intercept is 4.
Looking at the plotted points (0, 3) and (3, 2), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (3 - 0)
m = -1 / 3
The calculated slope is -1/3, which matches the slope in the equation y = -1/3x + 4.
Now, let's compare the y-intercept. The y-intercept of the equation is 4, which means the line should pass through the point (0, 4). However, the plotted line passes through the point (0, 3) instead of (0, 4).
Therefore, based on the y-intercept not matching, the plotted line on the graph is not the correct graph of y = -1/3x + 4.
Answer Choices are
Yes, it is the correct graph because this graph has a y-intercept of (0,4).Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .No, it is not the correct graph because this graph has a positive slope. No, it is not the correct graph because this graph has a positive slope. Yes, it is the correct graph because this graph has a y-intercept of (0,3).Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis. No, it is not the correct graph because this graph used (0,3) as the y-intercept.
Yes, it is the correct graph because this graph has a y-intercept of (0,4).Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .No, it is not the correct graph because this graph has a positive slope. No, it is not the correct graph because this graph has a positive slope. Yes, it is the correct graph because this graph has a y-intercept of (0,3).Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis. No, it is not the correct graph because this graph used (0,3) as the y-intercept.
The y-intercept of the equation y = -1/3x + 4 is at the point (0, 4). The plotted point on the graph is (0, 3) instead of (0, 4). So the correct answer choice is:
No, it is not the correct graph because this graph has a y-intercept of (0,3).
No, it is not the correct graph because this graph has a y-intercept of (0,3).
y=23x−1.(1 point)ResponsesA coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis. Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis. Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
To find if the line on the graph matches the equation y = 2/3x - 1, we need to check if the plotted points (0, -2) and (1, -9) satisfy the equation.
Let's check the slope from the plotted points:
m = (-9 - (-2)) / (1 - 0) = -7 / 1 = -7
The equation y = 2/3x - 1 has a slope of 2/3, so the slope doesn't match with the plotted points, indicating that the line doesn't match the equation.
Therefore, the correct answer is:
No, it is not the correct graph because the slope of the line on the graph does not match the slope of the equation y = 2/3x - 1.
Let's check the slope from the plotted points:
m = (-9 - (-2)) / (1 - 0) = -7 / 1 = -7
The equation y = 2/3x - 1 has a slope of 2/3, so the slope doesn't match with the plotted points, indicating that the line doesn't match the equation.
Therefore, the correct answer is:
No, it is not the correct graph because the slope of the line on the graph does not match the slope of the equation y = 2/3x - 1.
Which answer choice though
The correct answer choice based on the analysis is:
No, it is not the correct graph because the slope of the line on the graph does not match the slope of the equation y = 2/3x - 1.
No, it is not the correct graph because the slope of the line on the graph does not match the slope of the equation y = 2/3x - 1.
What are the plot points that make it not that answer
The given equation is y = 2/3x - 1. This equation represents a line with a slope of 2/3 and a y-intercept of -1.
The plotted points in the scenario are (0, -2) and (1, -9). To verify if they match the equation y = 2/3x - 1:
1. Substitute the x and y values of the first point (0, -2) into the equation:
-2 = 2/3(0) - 1
-2 = -1
This shows that the point (0, -2) does not satisfy the equation.
2. Substitute the x and y values of the second point (1, -9) into the equation:
-9 = 2/3(1) - 1
-9 = 2/3 - 1
-9 = 2/3 - 3/3
-9 = -1/3
This shows that the point (1, -9) also does not satisfy the equation.
Since both plotted points do not satisfy the equation y = 2/3x - 1, it confirms that the line does not match the equation.
The plotted points in the scenario are (0, -2) and (1, -9). To verify if they match the equation y = 2/3x - 1:
1. Substitute the x and y values of the first point (0, -2) into the equation:
-2 = 2/3(0) - 1
-2 = -1
This shows that the point (0, -2) does not satisfy the equation.
2. Substitute the x and y values of the second point (1, -9) into the equation:
-9 = 2/3(1) - 1
-9 = 2/3 - 1
-9 = 2/3 - 3/3
-9 = -1/3
This shows that the point (1, -9) also does not satisfy the equation.
Since both plotted points do not satisfy the equation y = 2/3x - 1, it confirms that the line does not match the equation.