Question

A line passes through the points (−3, 7) and (4, −2). Use this information for questions 1 through 3. 1. Find the slope of the line. Show your work. 2. Write the equation of the line in point-slope form. 3. Rewrite the equation of the line in standard form.

Answer 1

1.
`-(9)/(7)`

2.
`y-7=-(9)/(7) (x+3)`

3.
`y=-(9)/(7) x+(22)/(7)`

Explanation:

`(-3, 7)(4,-2)`

1. Find the slope of the line.

m = slope

slope formula:
`(y_2-y_1)/(x_2-x_1)`

`m = (-2-7)/(4-(-3))`

`m = (-9)/(7)`

The slope of the line is
`-(9)/(7)`

2. Write the equation of the line in point-slope form.

point-slope form:
`y-y_1=m(x-x_1)`

Use the given point (-3, 7) to substitute for
`x_1` and
`y_1` and the slope with m

`y-7=-(9)/(7) (x+3)`

3. Rewrite the equation of the line in standard form.

`y=-(9)/(7) x+b` Where b is the y-intercept of the line

Plug in any point to solve for b

`(7)=-(9)/(7)(-3)+b`

`7=(27)/(7) +b`

`b=7-(27)/(7)`

`b=(49)/(7) -(27)/(7) =(22)/(7)`

The equation of the line in standard form is
`y=-(9)/(7) x+(22)/(7)`