Questions: Choose the graph that matches the following system of equations:
x-3y=-12
2x-y=1
Transcript text: Choose the graph that matches the following system of equations:
\[
\begin{array}{l}
x-3 y=-12 \\
2 x-y=1
\end{array}
\]
Solution
Solution Steps
Step 1: Rewrite the equations in slope-intercept form.
The first equation, x - 3y = -12 can be rewritten as:
-3y = -x - 12
y = (1/3)x + 4
The second equation, 2x - y = 1 can be rewritten as:
-y = -2x + 1
y = 2x - 1
Step 2: Identify the slope and y-intercept of each equation.
For the first equation, y = (1/3)x + 4, the slope is 1/3 and the y-intercept is 4.
For the second equation, y = 2x - 1, the slope is 2 and the y-intercept is -1.
Step 3: Compare the graphs with the equations.
The first graph shows lines that roughly correspond to the calculated slopes and y-intercepts. The red line has a positive y-intercept around 4 and shallow positive slope, while the blue line has a negative y-intercept close to -1 and a steeper positive slope.
The second graph doesn't match.