Question

Find the equation of the line that is parallel to the graph of y=3x-2 and has the y-intercept (0,3)?

Answer 1

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y -intercept.

Given line y  = 3x -2

Compare the equation with slope-intercept form y = mx + b.

slope = 3 and y -intercept is -2.

y -intercept is -2, so the line crosses the y -axis at (0, -2)

Using slope find the next point.

Slope = rise/run = 3

Start at point (0, -2), move 3 units up and 1 unit right, then plot the point (1, 1).

Draw a line through these points.

We know that parallel line slopes are equal.

So the parallel line slope = 3 and given y -intercept is (0 , 3).

y -intercept is 3, so the parallel line crosses the y -axis at (0, 3).

Using slope find the next point.

Slope = rise/run = 3

Start at point (0, 3), move 3 units up and 1 unit right, then plot the point (1, 6).

Draw a line through these points.

Graph :

Required line equation is y  = 3x + 3.