Question

A line is parallel to y = 5x + 3 and

intersects the point (3,9).
What is the equation of this
parallel line?
y = [?]X + [ ]
Hint: Use the Point-Slope Form: y - y1 = m(x – x1)
Then write the equation in slope-intercept form.

Answer 1

y = 5x -6

Explanation:

The parallel line will have the same slope. We can rearrange the slope-intercept equation to let us solve for the y-intercept:

y = mx +b . . . . . . . slope-intercept equation

b = y - mx . . . . . . . . solved for b

b = 9 -5(3) = -6

Then the equation of the parallel line is ...

y = 5x -6

_____

Additional comment

If you use the hint, your point-slope equation is ...

y -9 = 5(x -3)

y = 5x -15 +9 . . . . eliminate parentheses, add 9

y = 5x -6 . . . . . . simplified

Answer 2

y = 5x - 6

Explanation:

y = 5x + 3

y = 5x + b

9 = 5(3) + b

9 = 15 + b

-15 -15

-6 = b

y = mx + b

y = 5x - 6

Hope this helps!