The graph of y = -3x - 8 for the given points (-2,-2), (-4,4) can be seen in the first image attached below. The correct graph of x-intercept = -1, y-intercept = -3 can be seen in the second image below.
Writing linear equation and representing them on graph.
Linear equation can be written in slope-intercept form; y = mx + b. To represent in slope-intercept form, you can be given two points on the graph, or the graph itself. It is equally important for you to know how to translate them effectively.
From the information given to us; we have two points of x and y values (-2, -2), (-4,4). The first thing to do in this situation is to determine the slope:
Slope (m) = -3
To find the y-intercept (b) using the general slope intercept form:
y = mx + b
Using one of the points given (-2,-2)
-2 = -3(-2) + b
-2 = 6 + b
-2 - 6 = b
b = -8
Therefore, the linear equation can be written as y = -3x - 8. The graph of y = -3x - 8 can be seen in the first image attached below.
For the second question; x-intercept = -1, y-intercept = -3. The xy points can be formulate as (-1,0) and (0,-3) from the intercepts given.
Slope (m) = -3
Using the point (-1,0)
y = mx + b
0 = -3(-1) + b
0 = 3 + b
b = -3
Therefore, the linear equation for the function is y = -3x - 3. The graph of the equation can be seen in the second image attached below.