Question

which points lie on the line that passes through point p and is parallel to the given line? select three options. (-4, 2) (-1, 3) (-2, 2) (4, 2) (-5, -1)

Explanation:

Step1: Find the slope of the given line

Pick two points on the given line, say $(1, - 1)$ and $(4,2)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2-( - 1)}{4 - 1}=\frac{3}{3}=1$. Since parallel lines have the same slope, the line passing through point $P(0,4)$ also has a slope of $1$.

Step2: Use the point - slope form of a line

The point - slope form is $y - y_1=m(x - x_1)$. Here $x_1 = 0,y_1 = 4,m = 1$, so the equation of the line is $y-4=1\times(x - 0)$, which simplifies to $y=x + 4$.

Step3: Check each point

For $(-4,2)$: Substitute $x=-4$ into $y=x + 4$, we get $y=-4 + 4=0
eq2$, so it does not lie on the line.
For $(-1,3)$: Substitute $x=-1$ into $y=x + 4$, we get $y=-1 + 4=3$, so it lies on the line.
For $(-2,2)$: Substitute $x=-2$ into $y=x + 4$, we get $y=-2 + 4=2$, so it lies on the line.
For $(4,2)$: Substitute $x = 4$ into $y=x + 4$, we get $y=4 + 4=8
eq2$, so it does not lie on the line.
For $(-5,-1)$: Substitute $x=-5$ into $y=x + 4$, we get $y=-5 + 4=-1$, so it lies on the line.

Answer:

B. $(-1,3)$
C. $(-2,2)$
E. $(-5,-1)$