Question

Write an equation in slope intercept form for the line that goes through the points ; (3,7) and (-1,9)

Answer 1

`y = -(1)/(2) x + (17)/(2)`

Explanation:

Pre-Solving

We are given that a line passes through the points (3, 7) and (-1, 9).

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

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Solving

Slope

We can start with the slope (m); it can be found using the formula
`(y_2-y_1)/(x_2-x_1)`, where
`(x_1,y_1)` and
`(x_2,y_2)` are points.

Although we already know the values of the points, we can label them to avoid confusion and mistakes.

`x_1=3\\y_1=7\\x_2=-1\\y_2=9`

Now, we can find the slope:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(9-7)/(-1-3)`

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

`m = (1)/(-2)`

The slope of the line is -1/2.

We can plug that into the formula for slope-intercept:

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

We now need to solve for b.

Since (3,7) and (-1,9) pass through the line, we can use either one of them to help solve for b.

Taking (3,7) for instance:

`7 = -(1)/(2) (3) + b`

Multiply

`7 = -(3)/(2) + b`

Add 3/2 to both sides.

`(17)/(2) = b`

Substitute 17/2 as b in the equation.

Our answer is:

`y = -(1)/(2) x + (17)/(2)`