Question

5. Please help. Which equation in slope-intercept form represents a line that is parallel to y=1/2x−2 and passes through the point (−8,1)?

Answer 1

Given:

The given equation of line is $y=\frac{1}{2}x-2$

The line passes through the point (-8,1)

We need to determine the equation of the line parallel to the line $y=\frac{1}{2}x-2$

Slope:

Since, the lines are parallel, the slope of the line is given by

$m=\frac{1}{2}$

Hence, the slope is $m=\frac{1}{2}$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (-8,1) and the slope $m=\frac{1}{2}$ in the above formula, we get;

$y-1=\frac{1}{2}(x+8)$

$y-1=\frac{1}{2}x+4$

     $y=\frac{1}{2}x+5$

Thus, the equation of the line is $y=\frac{1}{2}x+5$

Hence, Option C is the correct answer.