Equations of Linear Functions Quick Check
3 of 53 of 5 Items
Question
Use the table to answer the question.
x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point)
Responses
y=10x−2
y equals 10 x minus 2
y=10x+2
y equals 10 x plus 2
y=−10x+78
y equals negative 10 x plus 78
y=x+34
y equals x plus 34
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To find the equation of the linear function that models the relationship shown in the table, we need to find the slope-intercept form of the equation, y=mx+b, where m is the slope and b is the y-intercept.
Using the given points (4, 38) and (6, 58), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10
Now that we have the slope, we can substitute it into the slope-intercept form:
y = mx + b
y = 10x + b
To find b (the y-intercept), we can substitute one of the points into the equation:
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
So, the correct answer is:
y = 10x - 2