The equation of a function is y = -7x - 12. If this function were graphed, what would its slope be?
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The slope of the function can be determined by looking at the coefficient of "x" in the equation. In this case, the coefficient is -7. Therefore, the slope of the graph of this function would be -7.
x y
11 58
20 103
Write the equation of the linear function that models the relatioship shown in the table. ENter your answer in y = mx + b form.
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To find the equation of a linear function, we need to determine the values of the slope, represented by "m," and the y-intercept, represented by "b."
First, we need to calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Choosing the points (11, 58) and (20, 103), we can substitute their coordinates into the formula to find the slope:
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now, we have the value of the slope, which is 5.
To find the y-intercept, we can substitute the coordinates of one of the points (11, 58) into the equation y = mx + b, and solve for "b":
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
So, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3
(2,4)
(-3,-1)
Write the equation of the linear function shown on the graph. Enter your answer in y = mx + b form.
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To find the equation of the linear function, we need to determine the values of the slope, represented by "m," and the y-intercept, represented by "b."
First, we need to calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Choosing the points (2, 4) and (-3, -1), we can substitute their coordinates into the formula:
m = (-1 - 4) / (-3 - 2)
m = -5 / -5
m = 1
Now, we have the value of the slope, which is 1.
To find the y-intercept, we can substitute the coordinates of one of the points (2, 4) into the equation y = mx + b, and solve for "b":
4 = 1(2) + b
4 = 2 + b
b = 4 - 2
b = 2
So, the equation of the linear function shown on the graph is:
y = x + 2
Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y = mx + b form.
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To find the equation of the linear function, we need to determine the values of the slope, represented by "m," and the y-intercept, represented by "b."
First, we need to calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Choosing the points (6, 120) and (8, 156), we can substitute their coordinates into the formula:
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18
Now, we have the value of the slope, which is 18.
To find the y-intercept, we can substitute the coordinates of one of the points (6, 120) into the equation y = mx + b, and solve for "b":
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
So, the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns is:
y = 18x + 12