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1 answer:
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.)
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Answer:
Explanation:
To find the expression of the<em> high temperature of the day (T) as a function of the day (t)</em>, analyze the trend shown on the table.
The data in the column of the day (t) increases by 1, and the the data in the column of the high temperature increases by 1.
Thus, the slope is 1ºF per day.
The point-slope form of the equation of a line is:
Where m is the slope and y₁, x₁ are the coordinates of any point on the line.
Using the point (2, 96) you get:
Using the names T and t for y and x, respectively: