Question
Write the slope-intercept form of the line that has a slope of 2 and intersects the line 2x-3y=6 at x=3
. Include your work in your final answer.
. Include your work in your final answer.
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GPT 3.5
To find the y-intercept of the line 2x-3y=6, we need to substitute x=3 into the equation and solve for y:
2(3) - 3y = 6
6 - 3y = 6
-3y = 0
y = 0/(-3)
y = 0
So the y-intercept of the line 2x-3y=6 is (0,0).
Since the slope of the line we want to find is 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We know the slope (m=2) and the y-intercept (b=0), so the equation of the line is:
y = 2x + 0
y = 2x
2(3) - 3y = 6
6 - 3y = 6
-3y = 0
y = 0/(-3)
y = 0
So the y-intercept of the line 2x-3y=6 is (0,0).
Since the slope of the line we want to find is 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We know the slope (m=2) and the y-intercept (b=0), so the equation of the line is:
y = 2x + 0
y = 2x
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