Match the given information with the equation for the line.
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A line that contains the y-intercept (0, -2) and a slope of −34
A line that contains the point (0, -8) with a slope of 32
A line that contains the points (0, -2) and (4, 0).
A line that has a slope of 53
and a y-intercept of -4.
A line that contains the y-intercept (0, -2) and a slope of −34: y = -34x - 2
A line that contains the point (0, -8) with a slope of 32: y = 32x - 8
A line that contains the points (0, -2) and (4, 0): y = 1/2x - 2
A line that has a slope of 53 and a y-intercept of -4: y = 53x - 4
The equation for the line that contains the y-intercept (0, -2) and a slope of −34 is y = -34x - 2.
The equation for the line that contains the point (0, -8) with a slope of 32 is y = 32x - 8.
The equation for the line that contains the points (0, -2) and (4, 0) is y = 1/4x - 2.
The equation for the line that has a slope of 53 and a y-intercept of -4 is y = 53x - 4.
To match the given information with the equation for the line, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's go through each piece of information and find the corresponding equation for the line:
1. A line that contains the y-intercept (0, -2) and a slope of −34:
The equation for this line will be y = -34x - 2.
2. A line that contains the point (0, -8) with a slope of 32:
The equation for this line will be y = 32x - 8.
3. A line that contains the points (0, -2) and (4, 0):
First, let's find the slope using the formula m = (y2 - y1) / (x2 - x1).
m = (0 - (-2)) / (4 - 0) = 2 / 4 = 1/2.
Now, we can plug in the slope and one of the given points into the equation y = mx + b to find the y-intercept, b. Let's use the point (0, -2):
-2 = (1/2)(0) + b
-2 = b
So the equation for this line is y = (1/2)x - 2.
4. A line that has a slope of 53 and a y-intercept of -4:
The equation for this line will be y = 53x - 4.
So the final matching of information with equations is as follows:
A line that contains the y-intercept (0, -2) and a slope of −34 -> y = -34x - 2.
A line that contains the point (0, -8) with a slope of 32 -> y = 32x - 8.
A line that contains the points (0, -2) and (4, 0) -> y = (1/2)x - 2.
A line that has a slope of 53 and a y-intercept of -4 -> y = 53x - 4.