To graph the line with a slope of -2 and a y-intercept of -3, you start at the y-intercept (0, -3) on the Cartesian plane.
Since the slope is -2, this means that for every 1 unit you move to the right (the x-direction), you move 2 units down (the y-direction). You can plot another point using this slope:
- Start at (0, -3).
- Move 1 unit to the right to (1, -3), then move down 2 units to (1, -5). Plot the point (1, -5).
- Draw a line through these two points.
Now, we can check which of the given points lie on this line by substituting the x-values into the equation of the line. The equation of the line in slope-intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept) is:
\[y = -2x - 3\]
Now we evaluate each point:
-
(–2, 0):
\(y = -2(-2) - 3 = 4 - 3 = 1\) (not on the line, because y is 0) -
(–1.5, 0):
\(y = -2(-1.5) - 3 = 3 - 3 = 0\) (this point is on the line) -
(–6, 9):
\(y = -2(-6) - 3 = 12 - 3 = 9\) (this point is on the line) -
(2, –3):
\(y = -2(2) - 3 = -4 - 3 = -7\) (not on the line, because y is -3) -
(3, –9):
\(y = -2(3) - 3 = -6 - 3 = -9\) (this point is on the line) -
(–4, 4):
\(y = -2(-4) - 3 = 8 - 3 = 5\) (not on the line, because y is 4)
So, the points that lie on the line are:
- (–1.5, 0)
- (–6, 9)
- (3, –9)