Answer:
[tex]y=2x+3[/tex]
Step-by-step explanation:
We will first need to determine the slope of the line shown.
We know that it passes through the two points (-2, -2) and (1, 4).
Thus, we can use the slope formula to find the slope between the two points:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (-2, -2) be (x₁, y₁) and let (1, 4) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{4-(-2)}{1-(-2)}=\frac{6}{3}=2[/tex]
Hence, the slope of the original line was 2.
Since we want the new line to be parallel, the slope of the new line must also be 2.
We know that the slope is 2 and it passes through the point (2, 7).
So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We will substitute 2 for m. We will also let (2, 7) be (x₁, y₁). Substitute:
[tex]y-7=2(x-2)[/tex]
Solve for y. Distribute the right:
[tex]y-7=2x-4[/tex]
Add 7 to both sides. Hence, our equation is:
[tex]y=2x+3[/tex]
