Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 3$
$3x + y = -4$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$y = -3x - 4$

Step2: Find points for $y=\frac{1}{2}x+3$

When $x=0$, $y=3$; when $x=2$, $y=4$. Points: $(0,3), (2,4)$

Step3: Find points for $y=-3x-4$

When $x=0$, $y=-4$; when $x=-2$, $y=2$. Points: $(0,-4), (-2,2)$

Step4: Solve algebraically to find intersection

Set $\frac{1}{2}x+3 = -3x-4$
$\frac{1}{2}x + 3x = -4 - 3$
$\frac{7}{2}x = -7$
$x = -2$
Substitute $x=-2$ into $y=\frac{1}{2}x+3$: $y=\frac{1}{2}(-2)+3 = -1+3=2$

Answer:

The solution (intersection point) is $(-2, 2)$
To plot the lines:

1. For $y=\frac{1}{2}x+3$: click the points $(0, 3)$ and $(2, 4)$ to draw the line.
2. For $3x+y=-4$ (or $y=-3x-4$): click the points $(0, -4)$ and $(-2, 2)$ to draw the line.