Question

How do you graph $y+9=-3x$ and find the intercepts?

Answer 1

As we know that slope intercept form of a line is given as $y=mx+c$ where c is the y-intercept. To find the x intercept we will put the value of y equal to zero in the equation. Then we plot a graph by using the points of x intercept and y intercept.

Complete step-by-step solution:
We have been given an equation of line $y+9=-3x$.
We have to plot a graph and find the intercepts.
We know that the general form of slope intercept form of a line is given as $y=mx+c$ where, m is the slope and c is the y-intercept.
Now, we can rewrite the given equation as $y=-3x-9$
Now, comparing the above equation with the general form we will get
$m=-3$ and $c=-9$
So we get that the y intercept is at point $\left( 0,-9 \right)$.
Now, we know that for x-intercept $y=0$
Now, substituting the value of y in the given equation we will get
$\Rightarrow 0+9=-3x$
Simplifying the above obtained equation we will get
$\begin{aligned} & \Rightarrow 9=-3x \\\ & \Rightarrow x=\dfrac{9}{-3} \\\ & \Rightarrow x=-3 \\\ \end{aligned}$
So we get that the x intercept is at point $\left( -3,0 \right)$.
Hence we get the x intercept and y intercept as $-3,-9$ respectively.
Now, we can plot a graph by using the points $\left( -3,0 \right)$ and $\left( 0,-9 \right)$. Then we will get

Note: Students can find the other points also to easily plot a graph by substituting the value as $x=1$ in the given equation. Be careful while plotting the graph. Plot correct points and consider signs also, plot accordingly. Also remember the point that for x intercept the value of y is zero and for y intercept the value of x is zero.