The assignment was to draw a graph through the point (-5, -2) with a slope of 2. One student drew the graph below, but it was incorrect.

Answer 1

I'm sorry, but as an AI text-based model, I am unable to see or interpret images. However, I can help you understand how to correctly graph a line through the point (-5, -2) with a slope of 2.

To graph a line with a given slope and a point on the line, you can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

Where (x1, y1) represents the given point, and m represents the slope.

In this case, the given point is (-5, -2), and the slope is 2. Substituting these values into the equation, we get:

y - (-2) = 2(x - (-5))

Simplifying this equation gives:

y + 2 = 2x + 10

Now we can rearrange the equation into the standard slope-intercept form (y = mx + b):

y = 2x + 10 - 2

y = 2x + 8

Now, you can graph the line by plotting the given point (-5, -2) and using the slope to find additional points on the line.

Starting from the given point (-5, -2), use the slope, which is the ratio of the change in y (rise) to the change in x (run), to find another point. Since the slope is 2 (rise 2 units for every run 1 unit), you can move up 2 units and right 1 unit from the point (-5, -2) to find another point, which is (-4, 0).

Plot these two points (-5, -2) and (-4, 0) on a graph, and draw a straight line passing through both points. This line represents the graph of the equation y = 2x + 8, which is the correct graph for a line with a slope of 2 passing through the point (-5, -2).

Please note that without further information or the student's incorrect graph, I cannot provide specific feedback on their mistake.