How do you find the slope and intercept of y=3x+2?

May 4, 2016

color(blue)("the slope is 3 (taken from "3x)
$\textcolor{b l u e}{{x}_{\text{intercept}} = - \frac{2}{3}}$
$\textcolor{b l u e}{{y}_{\text{intercept}} = 2}$

Explanation:

color(blue)("the slope is 3 (taken from "3x)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(brown)(x_("Intercept")" is at y=0")

$\text{ } 0 = 3 x + 2$

$\textcolor{b r o w n}{\text{Subtract 2 from both sides}}$

$\text{ } 0 - 2 = 3 x + 2 - 2$

$\textcolor{b r o w n}{\text{But "0-2=-2" and } + 2 - 2 = 0}$

$\text{ } - 2 = 3 x$

$\textcolor{b r o w n}{\text{Divide both sides by 3}}$

$\text{ } - \frac{2}{3} = \frac{3}{3} \times x$

$\textcolor{b r o w n}{\text{But "3/3=1" and } 1 \times x = x}$

$\text{ } - \frac{2}{3} = x$

Write as $\textcolor{b l u e}{{x}_{\text{intercept}} = - \frac{2}{3}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(brown)(y_("intercept")" is at "x=0)

$\text{ } y = 3 \left(0\right) + 2$

$\textcolor{b r o w n}{\text{but } 3 \times 0 = 0}$

$\text{ } y = 0 + 2$

" "color(blue)(y_("intercept")=2)