Question

Point-slope form

Complete the point-slope equation of the line through (8, —8) and (9.8).
Use exact numbers.
y-8=

Answer 1

The equation in point-slope form is:

`y-\left(-8\right)=16\left(x-8\right)`

The equation of the line in slope-intercept form is:

`y=16x-136`

Explanation:

Given the points

(8, -8)

(9, 8)

Finding the slope between (8, -8) and (9, 8)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(8,\:-8\right),\:\left(x_2,\:y_2\right)=\left(9,\:8\right)`

`m=(8-\left(-8\right))/(9-8)`

`m=16`

Point slope form:

`y-y_1=m\left(x-x_1\right)`

Here:

m is the slope and (x₁, y₁) is the point

substituting the values m = 16 and the point (8, -8) in the point-slope form

`y-y_1=m\left(x-x_1\right)`

`y-\left(-8\right)=16\left(x-8\right)`

• Thus, the equation in point-slope form is:

`y-\left(-8\right)=16\left(x-8\right)`

now completing the point-slope form equation of the line

`y+8=16\left(x-8\right)`

subtract 8 from both sides

`y+8-8=16\left(x-8\right)-8`

`y=16x-136`

• Thus, the equation of the line in slope-intercept form is:

`y=16x-136`