Question

graph these equations:$y = -\frac{3}{2}x + 4$$y = -\frac{1}{4}x - 1$click to select points on the graph.

Explanation:

Step1: Find y-intercept of $y=-\frac{3}{2}x+4$

The y-intercept occurs at $x=0$:
$y = -\frac{3}{2}(0) + 4 = 4$
Point: $(0, 4)$

Step2: Find second point for $y=-\frac{3}{2}x+4$

Use $x=2$ (to eliminate fraction):
$y = -\frac{3}{2}(2) + 4 = -3 + 4 = 1$
Point: $(2, 1)$

Step3: Find y-intercept of $y=-\frac{1}{4}x-1$

The y-intercept occurs at $x=0$:
$y = -\frac{1}{4}(0) - 1 = -1$
Point: $(0, -1)$

Step4: Find second point for $y=-\frac{1}{4}x-1$

Use $x=4$ (to eliminate fraction):
$y = -\frac{1}{4}(4) - 1 = -1 - 1 = -2$
Point: $(4, -2)$

Answer:

For $y=-\frac{3}{2}x+4$, plot and connect $(0, 4)$ and $(2, 1)$ (extend the line across the grid).
For $y=-\frac{1}{4}x-1$, plot and connect $(0, -1)$ and $(4, -2)$ (extend the line across the grid).
The lines intersect at the solution point: solving $-\frac{3}{2}x+4 = -\frac{1}{4}x-1$ gives $x=4$, $y=-2$, so the intersection is $(4, -2)$.