Question

Write an equation of the line in slope-intercept form that passes through the point (-6, 1) and has a slope of ½.

Answer 1

`y = (1)/(2) x + 4`

Explanation:

Slope intercept form is:

`y = mx +b`

y and x remain as variables and don't get changed or touched.

m is the slope of the line.

b is the y-intercept of the line.

To find the information needed for this form, we need to use the equation:

`y - y_(1) = m (x - x_(1) )`

We are given that the slope is
`(1)/(2)`, so we plug it in for m:

`y - y_1 = (1)/(2) (x-x_1)`

Now, we need to plug in the given value of
`x_1` and
`y_1` in the point (-6, 1), where the x = -6 and y = 1. So it will look like this when plugged into the equation:

`y - 1 = (1)/(2) (x-(-6))`

Solve for y (isolate y on one side):

`y - 1 = (1)/(2) (x-(-6))\\\\y - 1 = (1)/(2) (x+6)\\\\y - 1 = (1)/(2) x+3\\\\\\y= (1)/(2)x+4`

Final answer is: y = 1/2x + 4

Answer 2

y = 1/2x +4

Explanation:

You are given the slope (m) of the line and a point, and asked for slope-intercept form:

y = mx +b . . . . . . . line with slope m and y-intercept b

The value of the intercept, b, can be found from the point by rearranging this equation to ...

b = y -mx

b = 1 -1/2(-6) = 4 . . . . using x=-6, y=1

Then the equation of the line with m=1/2 and b=4 is ...

y = 1/2x +4