# How do you find the x and y intercept of y = 3x – 8?

Feb 27, 2017

Solution provided in extreme detail.

${x}_{\text{intercept}} = \frac{8}{3}$

${y}_{\text{intercept}} = - 8$

#### Explanation:

$\textcolor{b l u e}{\text{Determin the y intercept}}$

Consider the standardised format of $y = m x + c$

$\textcolor{b l u e}{{y}_{\text{intercept}} = c = - 8}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the x intercept}}$

The x-intercept is when y = 0 because that is the value of y where the x-axis crosses it

Set y = 0 giving:$\text{ } 0 = 3 x - 8$

Add $\textcolor{red}{8}$ to both sides

$\textcolor{g r e e n}{0 \textcolor{red}{+ 8} \text{ "=" } 3 x - 8 \textcolor{red}{+ 8}}$

But $- 8 + 8 = 0$ giving:

$8 = 3 x$

Divide both sides by $\textcolor{red}{3}$

$\textcolor{g r e e n}{\frac{8}{\textcolor{red}{3}} = \frac{3}{\textcolor{red}{3}} x}$

But $\frac{3}{3} = 1 \mathmr{and} 1 \times x = x$ giving:

$\frac{8}{3} = x$

Write as $\textcolor{b l u e}{{x}_{\text{intercept}} = \frac{8}{3}}$