The equation for line j can be written as y= 1/8x+7. Parallel to line j is line k, which passes through the point ( – 3, – 1). Write the equation in slope-intercept form.

Question

 What is the equation of line k?

Answer 1

The equation for line j can be written as y= 1/8x+7. Parallel to line j is line k, which passes through the point (–3, –1). Write the equation in slope-intercept form. What is the equation of line k?

Detailed Solution:

Given/Known: Equation for line j: y = (1/8)x + 7 m₁ = 1/8 line j is parallel to line k m₂ = 1/8

Equation for line k: y = m₂x + b (x, y) = ( –3, –1).

y = m₂x + b

y = (1/8)x + b

–1 = (1/8)(–3) + b ==> –1 = –3/8 + b ==> –1 + 3/8 = b ==> b = –5/8

y = (1/8)x – 5/8 <== Final Answer

Answer 2

The equation for line k has a form y = ax + b. Here a - is the slope of the second line k which is parallel to line j. So, it has the same slope as that line j has.

We can write a = 1/8.

To find the value of b, we will use the fact that line k passes through the point with x = - 3 and y = - 1.

Plugging in the numbers, we will get: - 1 = (1/8) (-3) + b

Solving against b we will have b = - 5/8

And the line k could be described by equation y = (1/8) x - 5/8

Answer: y = (1/8) x - 5/8