Question

write an equation of a line that passes through the point t(-2, -5) and is parallel to the line y = 5x+7. f. y + 5 = -\frac{1}{5}(x + 2) g. y - 5 = 5(x - 2) h. y + 5 = 5(x + 2) j. y - 5 = 5(x + 2)

Explanation:

Step1: Recall slope - parallel lines property

Parallel lines have the same slope. The slope of the line $y = 5x+7$ is $m = 5$.

Step2: Use point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Given the point $T(-2,-5)$ and $m = 5$, we substitute $x_1=-2$, $y_1=-5$ and $m = 5$ into the point - slope form.
We get $y-(-5)=5(x - (-2))$, which simplifies to $y + 5=5(x + 2)$.

Answer:

H. $y + 5=5(x + 2)$