Question

Write a rule for the linear function in the graph.

Answer 1

3=4m+ b
-1=3m+b

m=4
plug in to either equation,
3=16+ b
b=-13

Thus, C would be the answer.

Answer 2

Answer:  The correct option is (C) $y=4x-13.$

Step-by-step explanation:  We are given to write a rule for the linear function given in the graph.

Since the graph is a straight line, so we are to find the equation of the line to find the rule.

From the graph, we note that

the points (3, -1) and (4, 3) lie on the straight line.

So, the slope of the line will be

$m=\dfrac{3-(-1)}{4-3}\\\\\\\Rightarrow m=4.$

Since the line passes through the point (4, 3), so the equation of the line is given by

$y-3=m(x-4)\\\\\Rightarrow y-3=4(x-4)\\\\\Rightarrow y=4x-16+3\\\\\Rightarrow y=4x-13.$

Thus, the required rule for the linear function is

$y=4x-13.$

Option (C) is correct.