Question

solve the following system of equations graphically on the set of axes below.
$y = -dfrac{1}{2}x + 8$
$y = 2x - 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=-\frac{1}{2}x+8$

• y-intercept: Set $x=0$, $y=8$ → point $(0,8)$
• x-intercept: Set $y=0$, $0=-\frac{1}{2}x+8$ → $x=16$ (we can use $x=2$, $y=-\frac{1}{2}(2)+8=7$ → point $(2,7)$ for plotting)

Step2: Find intercepts for $y=2x-7$

• y-intercept: Set $x=0$, $y=-7$ → point $(0,-7)$
• x-intercept: Set $y=0$, $0=2x-7$ → $x=3.5$ (we can use $x=4$, $y=2(4)-7=1$ → point $(4,1)$ for plotting)

Step3: Find intersection algebraically

Set $-\frac{1}{2}x+8=2x-7$
$8+7=2x+\frac{1}{2}x$
$15=\frac{5}{2}x$
$x=15\times\frac{2}{5}=6$
Substitute $x=6$ into $y=2x-7$: $y=2(6)-7=5$

Answer:

The solution (intersection point) is $(6, 5)$
To plot:

1. For $y=-\frac{1}{2}x+8$: mark $(0,8)$ and $(2,7)$, draw the line through them.
2. For $y=2x-7$: mark $(0,-7)$ and $(4,1)$, draw the line through them. The lines cross at $(6,5)$.