Question

Find the equation of the line that passes through the following two points: (3, -7) and (7, 2)

Answer 1

`y=(9)/(4)x-(55)/(4)`

Explanation:

Slope-intercept form: y = mx + b

Slope formula:
`(y2-y1)/(x2-x1)`

Given points: (3, -7), (7, 2)

(3, -7) = (x1, y1)

(7, 2) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

`(2-(-7))/(7-3)`

Simplify:

2 - (-7) = 2 + 7 = 9

7 - 3 = 4

`(9)/(4)`

The slope is
`(9)/(4)`.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (7, 2)) into the equation and solve for b:

`2=(9)/(4)(7)+b`

`2=(63)/(4)+b`

`-(55)/(4) =b`

The y-intercept is
`-(55)/(4)`.

Now that we know the slope and the y-intercept, we can write the equation:

`y=(9)/(4)x-(55)/(4)`