Question
Identify the slope and y intercept. Then, graph the linear equation. y−5=−3x
Answers
GPT 3.5
The given equation is y - 5 = -3x.
To identify the slope and y-intercept, we need to convert the given equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
To do this, we isolate the y variable by adding 5 to both sides of the equation:
y - 5 + 5 = -3x + 5
y = -3x + 5
Comparing it with the slope-intercept form, we find that the slope (m) is -3 and the y-intercept (b) is 5.
Now we can graph the linear equation.
To graph the line, we start by plotting the y-intercept, which is the point (0, b) on the coordinate plane. In this case, the y-intercept is 5, so the point is (0, 5).
Next, we use the slope to find any other points on the line. Since the slope is -3, which is negative, we can use the rule that a negative slope means the line goes downhill (from left to right) on the graph.
To find the next point, we move 1 step to the right (due to the positive x coefficient) and 3 steps down (due to the negative y coefficient) from the y-intercept.
Thus, we plot the point (1, 2), which lies on the line.
Now we can draw the line passing through the two points (0, 5) and (1, 2).
The graph of the linear equation y - 5 = -3x is a line passing through the points (0, 5) and (1, 2), with a slope of -3.
Here is the graph:
[image of line passing through the points (0, 5) and (1, 2), with a downward slope]
To identify the slope and y-intercept, we need to convert the given equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
To do this, we isolate the y variable by adding 5 to both sides of the equation:
y - 5 + 5 = -3x + 5
y = -3x + 5
Comparing it with the slope-intercept form, we find that the slope (m) is -3 and the y-intercept (b) is 5.
Now we can graph the linear equation.
To graph the line, we start by plotting the y-intercept, which is the point (0, b) on the coordinate plane. In this case, the y-intercept is 5, so the point is (0, 5).
Next, we use the slope to find any other points on the line. Since the slope is -3, which is negative, we can use the rule that a negative slope means the line goes downhill (from left to right) on the graph.
To find the next point, we move 1 step to the right (due to the positive x coefficient) and 3 steps down (due to the negative y coefficient) from the y-intercept.
Thus, we plot the point (1, 2), which lies on the line.
Now we can draw the line passing through the two points (0, 5) and (1, 2).
The graph of the linear equation y - 5 = -3x is a line passing through the points (0, 5) and (1, 2), with a slope of -3.
Here is the graph:
[image of line passing through the points (0, 5) and (1, 2), with a downward slope]