9514 1404 393
Answer:
see attached
Step-by-step explanation:
The attachment lists points on each graph.
a) The equation for a horizontal line is ...
y = constant
Here, the output value is always 5, so that is the constant in the equation:
y = 5
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b) The graph is a straight line through the origin, so the equation is that of a proportion:
y = kx . . . . . for some constant of proportionality k
Using the point (x, y) = (-4, 2), we can find k from ...
k = y/x = 2/(-4) = -1/2
The equation of the line is ...
y = -1/2x
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c) The graph has a rise of 3 units for each run of 1 unit, so the slope is ...
m = rise/run = 3/1 = 3
The y-intercept (where the line crosses the y-axis) is b = -2. Then the slope-intercept form of the equation is ...
y = mx + b . . . . . for slope m and y-intercept b
y = 3x - 2
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You can check that the equation is satisfied by each of the points listed. For example, ...
a) in = -4, out = y = 5 . . . matches table
b) in = 2, out = y = -1/2(2) = -1 . . . matches table
c) in = 1, out = y = 3(1) -2 = 1 . . . matches table
(You can check the other table values.)
