Question

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

`\displaystyle y=(1)/(2)x+5`

Explanation:

We want to find the slope in slope-intercept form of a line that is parallel to:

`\displaystyle y=(1)/(2)x-2`

And passes through the point (-8, 1).

Recall that parallel lines have equivalent slopes.

Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.

We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:

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

Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:

`\displaystyle y-(1)=(1)/(2)(x-(-8))`

Since we want the equation in slope-intercept form, we can isolate y. Distribute:

`\displaystyle y-1=(1)/(2)x+4`

Therefore, our equation is:

`\displaystyle y=(1)/(2)x+5`