Question

write in slope intercept form and identity the slope and y intercept. a. x/3 + y/2 = 1b. 4x -3y + 2 =0c. x - y = 5(x - y)

Answer 1

Consider that the slope-intercept form of the straight line with slope (m) and y-intercept (c) is given by,

$y=mx+c$

a.

Modify the given equation as,

$\begin{gathered} \frac{x}{3}+\frac{y}{2}=1 \\ \frac{y}{2}=-\frac{x}{3}+1 \\ y=-\frac{2}{3}x+2 \end{gathered}$

Thus, the equation in slope-intercept form can be written as,

$y=-\frac{2}{3}x+2$

b.

Modify the given equation as,

$\begin{gathered} 4x-3y+2=0 \\ 3y=4x+2 \\ y=\frac{4}{3}x+\frac{2}{3} \end{gathered}$

Thus, the equation in slope-intercept form can be written as,

$y=\frac{4}{3}x+\frac{2}{3}$

c.

Modify the given equation as,

$\begin{gathered} x-y=5(x-y) \\ x-y=5x-5y \\ 5y-y=5x-x \\ 4y=4x \\ y=x \end{gathered}$

Thus, the equation in slope-intercept form can be written as,

$y=x$