which points lie on the line that passes through point p and is parallel to the given line? select three…

Explanation:

Step1: Find the slope of the given line

Pick two points on the given line, say $(0, - 2)$ and $(2,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-2)}{2 - 0}=1$.

Step2: Use the point - slope form

Point $P$ has coordinates $(0,4)$. The equation of the line parallel to the given line (same slope $m = 1$) passing through $P(0,4)$ using the point - slope form $y - y_1=m(x - x_1)$ is $y-4=1(x - 0)$, which simplifies to $y=x + 4$.

Step3: Check each point

For point $(-4,2)$: Substitute $x=-4$ into $y=x + 4$, we get $y=-4 + 4=0\neq2$. For point $(-1,3)$: Substitute $x=-1$ into $y=x + 4$, we get $y=-1 + 4=3$. For point $(-2,2)$: Substitute $x=-2$ into $y=x + 4$, we get $y=-2+4 = 2$. For point $(4,2)$: Substitute $x = 4$ into $y=x + 4$, we get $y=4 + 4=8\neq2$. For point $(-5,-1)$: Substitute $x=-5$ into $y=x + 4$, we get $y=-5 + 4=-1$.

Answer:

$(-1,3),(-2,2),(-5,-1)$