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 $y + 2=4(x + 5)$, expand the right - hand side: $y+2 = 4x+20$. Then, isolate $y$ by subtracting 2 from both sides: $y=4x + 18$. The slope $m = 4$ and the y - intercept is $(0,18)$.

Step2: Use the point - slope form concept

The given point $(-5,-2)$ satisfies the original point - slope form $y+2 = 4(x + 5)$. To graph the line, start by plotting the point $(-5,-2)$.

Step3: Use the slope to find another point

Since the slope $m = 4=\frac{4}{1}$, from the point $(-5,-2)$, move 1 unit to the right and 4 units up. We get to the point $(-5 + 1,-2+4)=(-4,2)$.

Step4: Draw the line

Draw a straight line passing through the points $(-5,-2)$ and $(-4,2)$.

Answer:

The graph of the line $y + 2=4(x + 5)$ is a straight line with slope 4 passing through the point $(-5,-2)$.