slope of parallel line

Question

Write the equation of the line that is parallel to y = 5x + 2 and passes through the point (1, 4). Write your answer in slope-intercept form.

 

Answer 1

The slope- intercept form for the equation of a line is written as: y = mx + b where m is the slope and b is the y-intercept. The slopes of parallel lines are always the same.

For this problem where the equation is y = 5x + 2, the slope is 5 and the y-intercept is 2 .

The slope of a parallel line would also be 5: y = 5x + b

We can write the equation of a line parallel to this one but passing through the point (1,4) by substituting these coordinates for x and y and solving for b for the parallel line:

y = 5x + b

4 = 5 • 1 + b

4 = 5 + b

4 - 5 = 5 + b - 5

-1 = b

The Y-intercept of the parallel line is -1.

So the equation of the parallel line with the same slope is: y = 5x -1