Question

Which linear function has a graph that includes all of the points in the table?

х
у
-22
-3
-1
-12
o
-7
2
3
13
Of(x) = -5x - 7
Of(x) = 5x - 7
f(x) = 2x + 6
O f(x) = -23 + 6

Answer 1

B. f(x) = 5x - 7

Explanation:

✔️Using the table of values given, find the slope (m) and y-intercept (b) of the line of the graph that represents the table, then write the function in slope-intercept form.

✔️Slope (m) using (0, -7) and (2, 3):

Slope (m) = ∆y/∆x

Slope (m) = (3 -(-7))/(2 - 0)

Slope (m) = 10/2

Slope (m) = 5

✔️ y-intercept (b):

b = -7, because where x = 0, y = -7, which is the point where the y-axis is intercepted by the line of the graph.

✔️Write the linear function in slope-intercept form by substituting m = 5 and b = -7 into f(x) = mx + b

Thus:

f(x) = 5x + (-7)

f(x) = 5x - 7

Therefore, the linear function that has a graph that includes all the points in the table would be f(x) = 5x - 7.