Question

What would the answers to these be?

Answer 1

The first equation, 8x - 9y = - 23

Obtain the equation in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = ( $\frac{1}{2}$, 3) and (x₂, y₂ ) = (- 4, - 1 )

m = $\frac{-1-3}{-4-1/2}$ = (- 4)/- $\frac{9}{2}$ = $\frac{8}{9}$

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

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

using (- 4, - 1 ), then

- 1 = - $\frac{32}{9}$ + c ⇒ c = $\frac{23}{9}$

y = $\frac{8}{9}$ x +$\frac{23}{9}$ ← in slope- intercept form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange the slope- intercept equation into this form

multiply through by 9

9y =  8x + 23 ( subtract 9y and 23 from both sides )

8x - 9y = - 23 in standard form