Question

1- A given line as a slope of – and y-intercept of 8. Which equation represents a line4that is parallel to the given line and passes through the point (-8,-2)?

Answer 1

Answer:

y=(1/4)x.

Explanation:

Two lines are parallel if their slopes are equal.

The slope of the given line is 1/4, therefore:

• The slope of the new line = 1/4

Thus, the goal is to find the equation of a line with a slope of 1/4 that passes through (-8,-2).

Using the point-slope formula:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{4}(x-(-8)) \\ y+2=\frac{1}{4}(x+8) \\ y+2=\frac{1}{4}x+2 \\ y=\frac{1}{4}x+2-2 \\ y=\frac{1}{4}x \end{gathered}$

The equation of the line is y=(1/4)x.

The 3rd choice is correct.