# How do you graph using the intercepts for 4x+3y=-5?

Mar 6, 2016

$\textcolor{b l u e}{{y}_{\text{intercept}} = - \frac{5}{3}}$
color(blue)(x_("intercept") =-5/4

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{4 x + 3 y = - 5}$......................(1)

$\textcolor{b l u e}{\text{To find the x-intercept}}$
The x-axis crosses the y-axis at $y = 0$ so all we need to do is substitute 0 for y and we are then able to determine x-intercept

Write equation (1) as $\text{ } 4 x + 3 \left(0\right) = - 5$

Divide both sides by 4 giving

$\frac{4}{4} x = - \frac{5}{4}$

But $\frac{4}{4} = 1$

color(blue)(x_("intercept") =-5/4

$\textcolor{b l u e}{\text{To find the y-intercept}}$
The y-axis crosses the x-axis at $x = 0$ so all we need to do is substitute 0 for x and we are then able to determine y-intercept

Write equation (1) as $\text{ } 4 \left(0\right) + 3 y = - 5$

Divide both sides by 3 giving

$\text{ } \frac{3}{3} y = - \frac{5}{3}$

But $\frac{3}{3} = 1$

" "color(blue)(y_("intercept")=-5/3)
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$\textcolor{b l u e}{\text{Drawing the graph}}$

Put a mark on the x axis at $x = - \frac{5}{4}$
Put a mark on the y axis at $y = - \frac{5}{3}$

Put a ruler on the graph and draw a line that passes through both these points. Extend the line to the edges of the graph.

$\textcolor{red}{\text{////////////////////////////////////////////////////////////////////////////}}$
$\textcolor{g r e e n}{\text{If you so wish to, this is how you change the equation into the format of}}$

$\text{ } y = m x + c$

Subtract $\textcolor{b l u e}{4 x}$ from both sides

" "color(brown)(4xcolor(blue)(-4x)+3y=-5color(blue)(-4x)

$\text{ } 0 + 3 y = - 4 x - 5$

Divide both sides by (same as $\textcolor{b l u e}{\times \frac{1}{3}} \text{)}$

$\text{ } \textcolor{b r o w n}{3 y \textcolor{b l u e}{\times \frac{1}{3}} = \left(- 4 x - 5\right) \textcolor{b l u e}{\times \frac{1}{3}}}$

$\text{ } \frac{3}{3} \times y = - \frac{4}{3} x - \frac{5}{3}$

But $\frac{3}{3} = 1$ giving

$\text{ } y = - \frac{4}{3} x - \frac{5}{3}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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