Question

Using the following two points, what is the linear equation in standard and slope-intercept form? (5,-7), (-3,2)​

Answer 1

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (5, - 7 ) and (x₂, y₂ ) = (- 3, 2 )

m = $\frac{2-(-7)}{-3-5}$ = $\frac{2+7}{-8}$ = - $\frac{9}{8}$ , then

y = - $\frac{9}{8}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 3, 2 )

2 = $\frac{27}{8}$ + c ⇒ c = 2 - $\frac{27}{8}$ = $\frac{16}{8}$ - $\frac{27}{8}$ = - $\frac{11}{8}$

y = - $\frac{9}{8}$ x - $\frac{11}{8}$ ← equation in slope- intercept form

multiply through by 8 to clear the fractions

8y = - 9x - 11 ( add 9x to both sides )

9x + 8y = - 11 ← equation in standard form