# How do you graph -4y-3x=4?

Jun 22, 2018

See a solution process below:

#### Explanation:

First, solve for two points which solve the equation and plot these points:

First Point: For $x = 0$

$- 4 y - \left(3 \times 0\right) = 4$

$- 4 y - 0 = 4$

$- 4 y = 4$

$\frac{- 4 y}{\textcolor{red}{- 4}} = \frac{4}{\textcolor{red}{- 4}}$

$y = - 1$ or $\left(0 , - 1\right)$

Second Point: For $x = 4$

$- 4 y - \left(3 \times 4\right) = 4$

$- 4 y - 12 = 4$

$- 4 y - 12 + \textcolor{red}{12} = 4 + \textcolor{red}{12}$

$- 4 y - 0 = 16$

$- 4 y = 16$

$\frac{- 4 y}{\textcolor{red}{- 4}} = \frac{16}{\textcolor{red}{- 4}}$

$y = - 4$ or $\left(4 , - 4\right)$

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+1)^2-0.035)((x-4)^2+(y+4)^2-0.035)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(-4y-3x-4)(x^2+(y+1)^2-0.035)((x-4)^2+(y+4)^2-0.035)=0 [-10, 10, -5, 5]}

Jun 22, 2018

graph{-4y-3x=4 [-10, 10, -5, 5]}

#### Explanation:

Convert the equation $- 4 y - 3 x = 4$ into slope-intercept form to make it easier to graph.
Remember, slope-intercept form is $y = m x + b$, where $m$ stands for slope and $b$ stands for y-intercept.
This means you need to isolate $y$ in this equation $- 4 y - 3 x = 4$.
Add $3 x$ to both sides, which will give you $- 4 y = 3 x + 4$.
Divide by $- 4$ on both sides and you will get $y = - \frac{3}{4} x - 1$.
This means the y-intercept is -1 and the slope is $- \frac{3}{4}$.
On the graph, place a dot on $\left(0 , - 1\right)$ since that is the y-intercept and where you will start the graph.
Remember, slope is $\frac{r i s e}{r u n}$. So in this case, you go up 3 and to the left 4 starting from the y-intercept. And you go down 3 and to the right 4 starting from the y-intercept.