Answer:
The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.
To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:
y = x - b
To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:
-5 = 1(0) - b
b = -(-5)
b = 5
Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.
To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:
Graph of y = -3x - 5 (slope = -3, y-intercept = -5):
|
-5| x
| x
| x
| x
| x
| x
x---------------
-3 -2 -1 0 1 2 3
Graph of y = x - 5 (slope = 1, y-intercept = 5):
|
5| x
| x
| x
| x
| x
| x
x---------------
-5 -4 -3 -2 -1 0 1 2 3
As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.