Question

y = -\frac{2}{5}x - 1\
y = \frac{2}{5}x - 5\

1. click to select points on the graph.

Explanation:

Step1: Find y-intercept for first line

For $y = -\frac{2}{5}x - 1$, set $x=0$:
$y = -\frac{2}{5}(0) - 1 = -1$
So point is $(0, -1)$.

Step2: Find second point for first line

Set $x=5$:
$y = -\frac{2}{5}(5) - 1 = -2 - 1 = -3$
So point is $(5, -3)$.

Step3: Find y-intercept for second line

For $y = \frac{2}{5}x - 5$, set $x=0$:
$y = \frac{2}{5}(0) - 5 = -5$
So point is $(0, -5)$.

Step4: Find second point for second line

Set $x=5$:
$y = \frac{2}{5}(5) - 5 = 2 - 5 = -3$
So point is $(5, -3)$.

Step5: Find intersection point

Set equations equal:
$-\frac{2}{5}x - 1 = \frac{2}{5}x - 5$
$-\frac{2}{5}x - \frac{2}{5}x = -5 + 1$
$-\frac{4}{5}x = -4$
$x = (-4) \times (-\frac{5}{4}) = 5$
Substitute $x=5$ into first equation: $y=-3$, so intersection is $(5, -3)$.

Answer:

Points for $y = -\frac{2}{5}x - 1$: $(0, -1)$, $(5, -3)$
Points for $y = \frac{2}{5}x - 5$: $(0, -5)$, $(5, -3)$
Intersection point: $(5, -3)$