Question

graph this line:
y + 4 = -5(x + 8)
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -8 to 10, grid lines, and axes arrows)

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 4=-5(x + 8) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( m=-5 \) and the point \( (x_1,y_1)=(-8,-4) \).

Step2: Find another point using the slope

The slope \( m = - 5=\frac{-5}{1} \). Starting from the point \( (-8,-4) \), we can move 1 unit to the right (increase \( x \) by 1) and 5 units down (decrease \( y \) by 5). So, if \( x=-8 + 1=-7 \), then \( y=-4-5=-9 \). But we can also use the y - intercept method. Let's rewrite the equation in slope - intercept form (\( y=mx + b \)).
Expand the right - hand side: \( y+4=-5x-40 \).
Subtract 4 from both sides: \( y=-5x-44 \). When \( x = 0 \), \( y=-44 \) (but this point is not on the given graph). When \( x=-8 \), \( y=-4 \) (this is the point we identified from the point - slope form). When \( x=-7 \), \( y=-5\times(-7)-44 = 35 - 44=-9 \) (also not on the graph). Wait, maybe we made a mistake. Let's go back to the point - slope form. The point \( (-8,-4) \) is on the line. Let's check the graph. The x - axis ranges from - 10 to 10 and y - axis from - 8 to 10. Wait, the y - axis in the graph goes from - 8 to 10? Wait, the original graph has y - axis with 10 at the top and - 8 at the bottom? Wait, no, the user's graph: the y - axis has 10,8,6,4,2,0,-2,-4,-6,-8. So the point \( (-8,-4) \): x=-8, y=-4. Let's plot this point. x=-8 is on the x - axis (the vertical line x=-8) and y=-4 is on the y - axis (the horizontal line y=-4). The intersection of x=-8 and y=-4 is a point on the line. Then, using the slope \( m=-5 \), from \( (-8,-4) \), move 1 unit right (x=-7) and 5 units down (y=-9), but y=-9 is below the graph's visible y - range. Alternatively, move 1 unit left (x=-9) and 5 units up (y = 1). Let's check: if \( x=-9 \), then from the equation \( y+4=-5(-9 + 8)=-5\times(-1) = 5 \), so \( y=5 - 4 = 1 \). So the point \( (-9,1) \) is also on the line.

Answer:

To graph the line \( y + 4=-5(x + 8) \), plot the points \( (-8,-4) \) and \( (-9,1) \) (or other points found using the slope - point form or slope - intercept form) and draw a straight line through them. The key point from the point - slope form is \( (-8,-4) \), and another point can be found as follows: from \( (-8,-4) \), using the slope \( m = - 5 \), when \( x=-8+1=-7 \), \( y=-4-5=-9 \) (not in the visible graph range), when \( x=-8 - 1=-9 \), \( y=-4 + 5 = 1 \) (this point \( (-9,1) \) is in the graph's range). So the two points to plot are \( (-8,-4) \) and \( (-9,1) \) (and then draw the line through them).