Question

What is the equation of a line that has a slope of –1/2 and contains the point (8, 1)? Express the equation in slope-intercept form, y = mx + b.
A- y= -1/2x+5
B- y= -1/2x+4
C- y= -1/2x+8 1/2
D- y= -1/2x-5

Answer 1

Option A: $y=-\frac{1}{2} x+5$ is the equation of the line.

Explanation:

It is given that the equation has a slope is $m=-\frac{1}{2}$

It also contains the point $(8,1)$

We need to find the equation of line in slope - intercept form.

First, we shall determine the value of y - intercept(b).

Let us substitute the slope $m=-\frac{1}{2}$ and the point $(8,1)$ in the slope - intercept form $y=mx+b$ , we get,

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

Simplifying, we have,

$1=-4+b$

Adding both sides of the equation by 4, we have,

$1+4=b$

     $5=b$

Thus, the y - intercept is $b=5$

Now, substituting the slope $m=-\frac{1}{2}$ and the y - intercept $b=5$ in the slope - intercept form $y=mx+b$ , we get,

$y=-\frac{1}{2} x+5$

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

Hence, Option A is the correct answer.