Question

solve the following system of equations graphically on the set of axes below.
$y = -dfrac{5}{2}x - 4$
$y = dfrac{1}{2}x + 2$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=-\frac{5}{2}x-4$

• y-intercept (x=0): $y=-\frac{5}{2}(0)-4=-4$, so point $(0, -4)$
• x-intercept (y=0): $0=-\frac{5}{2}x-4 \implies \frac{5}{2}x=-4 \implies x=-\frac{8}{5}=-1.6$, so point $(-1.6, 0)$

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

• y-intercept (x=0): $y=\frac{1}{2}(0)+2=2$, so point $(0, 2)$
• x-intercept (y=0): $0=\frac{1}{2}x+2 \implies \frac{1}{2}x=-2 \implies x=-4$, so point $(-4, 0)$

Step3: Solve algebraically for intersection

Set equations equal: $-\frac{5}{2}x-4=\frac{1}{2}x+2$
Combine like terms: $-\frac{5}{2}x-\frac{1}{2}x=2+4$
Simplify: $-3x=6 \implies x=-2$
Substitute $x=-2$ into $y=\frac{1}{2}x+2$: $y=\frac{1}{2}(-2)+2=-1+2=1$

Answer:

The solution (intersection point) is $(-2, 1)$
To graph:

1. For $y=-\frac{5}{2}x-4$, plot $(0, -4)$ and $(-1.6, 0)$, then draw the line through them.
2. For $y=\frac{1}{2}x+2$, plot $(0, 2)$ and $(-4, 0)$, then draw the line through them.

The lines cross at $(-2, 1)$.