To find the slope of the line, we calculate the change in y divided by the change in x between the two points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-1 - 2) / (1 - 0)
Slope = -3 / 1
Slope = -3
Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the points on the line, for example (0, 2):
y - 2 = -3(x - 0)
y - 2 = -3x
y = -3x + 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.
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 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.Write the equation of the line in slope-intercept form.(1 point)
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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 on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.Write the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points provided (0, -2) and (3, 0):
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
m = 2/3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Substitute the slope (m = 2/3) and the point (0, -2):
y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.
m = (y2 - y1) / (x2 - x1)
Using the points provided (0, -2) and (3, 0):
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
m = 2/3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Substitute the slope (m = 2/3) and the point (0, -2):
y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.
Given the equation y=−2x+2 , what is the slope? Write your answer as an integer.
The slope of the line represented by the equation y = -2x + 2 is -2.
Therefore, the slope of the line is -2.
Therefore, the slope of the line is -2.
Given the equation y=3/4x−2 what is the y -intercept? Write your answer as an ordered pair.
The y-intercept is the point where the line intersects the y-axis, which occurs when x = 0.
If we substitute x = 0 into the equation y = \(\frac{3}{4}x - 2\), we get:
y = \(\frac{3}{4}(0) - 2\) = 0 - 2 = -2
Therefore, the y-intercept is the point (0, -2).
If we substitute x = 0 into the equation y = \(\frac{3}{4}x - 2\), we get:
y = \(\frac{3}{4}(0) - 2\) = 0 - 2 = -2
Therefore, the y-intercept is the point (0, -2).
1 answer