Question

solve the following system of equations graphically on the set of axes below.
$y = -dfrac{1}{6}x + 7$
$y = 2x - 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=-\frac{1}{6}x+7$

For y-intercept ($x=0$):
$y = -\frac{1}{6}(0) + 7 = 7$ → point $(0, 7)$
For x-intercept ($y=0$):
$0 = -\frac{1}{6}x + 7$
$\frac{1}{6}x = 7$
$x = 42$ (use $x=6$ for a closer point: $y=-\frac{1}{6}(6)+7=6$ → $(6,6)$)

Step2: Find intercepts for $y=2x-6$

For y-intercept ($x=0$):
$y = 2(0) - 6 = -6$ → point $(0, -6)$
For x-intercept ($y=0$):
$0 = 2x - 6$
$2x = 6$
$x = 3$ → point $(3, 0)$

Step3: Solve algebraically to find intersection

Set equations equal:
$-\frac{1}{6}x + 7 = 2x - 6$
Multiply all terms by 6 to eliminate fraction:
$-x + 42 = 12x - 36$
$42 + 36 = 12x + x$
$78 = 13x$
$x = 6$
Substitute $x=6$ into $y=2x-6$:
$y = 2(6) - 6 = 6$

Answer:

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

1. For $y=-\frac{1}{6}x+7$: plot $(0,7)$ and $(6,6)$, draw a line through them.
2. For $y=2x-6$: plot $(0,-6)$ and $(3,0)$, draw a line through them. The lines cross at $(6,6)$.