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

Answer:

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:

$y=16x-136$

Step-by-step explanation:

Given the points

(8, -8)

(9, 8)

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

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{8-\left(-8\right)}{9-8}$

$m=16$

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:

$y=16x-136$