# How do you find the x and y intercept of 9x + 8y = −24?

Jul 11, 2016

${y}_{\text{intercept}} = - 3$

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

#### Explanation:

Convert the formula into the standard form of $y = m x + c$ for a straight line graph.

Subtract $\textcolor{b l u e}{9 x}$ from both sides

$\textcolor{b r o w n}{9 x \textcolor{b l u e}{- 9 x} + 8 y = - 24 \textcolor{b l u e}{- 9 x}}$

$8 y = - 9 x - 24$

Divide both sides by $\textcolor{b l u e}{8}$

$\textcolor{b r o w n}{\frac{8}{\textcolor{b l u e}{8}} \times y = - \frac{9}{\textcolor{b l u e}{8}} x - \frac{24}{\textcolor{b l u e}{8}}}$

But $\frac{8}{8} = 1 \text{ and } \frac{24}{8} = 3$ giving

$y = - \frac{9}{8} x - 3$
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$\textcolor{b l u e}{\text{Determine y intercept}}$

The line crosses the y-axis at $x = 0$ so by substitution

color(brown)(y=-9/8x-3)color(blue)(" "->" "y=-9/8(0)-3

${y}_{\text{intercept}} = - 3$
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$\textcolor{b l u e}{\text{Determine x intercept}}$

The line crosses the x-axis at $y = 0$ so by substitution

color(brown)(y=-9/8x-3)color(blue)(" "->" "0=-9/8x-3

$\frac{9}{8} x = - 3$

$x = {\cancel{\left(- 3\right)}}^{- 1} \times \frac{8}{{\cancel{9}}^{3}} \text{ " =" "- 8/3" " =" } - 2 \frac{2}{3}$

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