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=-(1)/(2) x+5` is the equation of the line.

Step-by-step explanation:

It is given that the equation has a slope is
`m=-(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=-(1)/(2)` and the point
`(8,1)` in the slope - intercept form
`y=mx+b` , we get,

`1=-(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=-(1)/(2)` and the y - intercept
`b=5` in the slope - intercept form
`y=mx+b` , we get,

`y=-(1)/(2) x+5`

Thus, the equation of the line is
`y=-(1)/(2) x+5`

Hence, Option A is the correct answer.