Question

1. y + 2 = 4(x + 5)

m = \frac{4}{1}, x=-5, y=-2 (-5,-2)

Explanation:

Step1: Rewrite the equation in slope - intercept form

Starting with $y + 2=4(x + 5)$, distribute the 4: $y+2 = 4x+20$. Then subtract 2 from both sides to get $y=4x + 18$.

Step2: Identify the slope and y - intercept

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $y = 4x+18$, the slope $m = 4$ and the y - intercept $b = 18$.

Step3: Use the point - slope form concept

The point - slope form is $y - y_1=m(x - x_1)$. We are given a point $(-5,-2)$ and slope $m = 4$. The equation $y+2 = 4(x + 5)$ is already in point - slope form with $(x_1,y_1)=(-5,-2)$ and $m = 4$. To graph, start at the point $(-5,-2)$.

Step4: Use the slope to find other points

Since the slope $m = 4=\frac{4}{1}$, from the point $(-5,-2)$, move 1 unit to the right and 4 units up to get another point. For example, from $(-5,-2)$ if we move 1 unit to the right (new $x=-5 + 1=-4$) and 4 units up (new $y=-2 + 4 = 2$), we get the point $(-4,2)$.

Answer:

The graph of the line $y + 2=4(x + 5)$ has a slope of 4 and passes through the point $(-5,-2)$. We can use the slope to find additional points to draw the line on the given coordinate grid.