Question

How do you write a linear function????????????? For those 2 problems?? (attached)

Answer 1

(9) The linear function is $y=\frac{1}{3}x+3$

(10) The linear function is $y=0x-7$

Explanation:

(9) The coordinates from the graph are (-6,1), (-3,2), (0,3) and (3,4)

Linear function:

The linear function can be determined using the formula,

$y=mx+b$

The y - intercept of the line is the value of y when x = 0.

Thus, from the graph, we have, $b=3$

Let us substitute the points (-6,1), (-3,2) in the slope formula,

$m=\frac{2-1}{-3+6}=\frac{1}{3}$

Thus, the slope is $m=\frac{1}{3}$

Substituting the value $m=\frac{1}{3}$ and $b=3$ in the formula $y=mx+b$ , we get,

$y=\frac{1}{3}x+3$

Thus, the linear function of the equation is $y=\frac{1}{3}x+3$

(10) Linear function:

The linear function can be determined using the formula,

$y=mx+b$

The y - intercept of the line is the value of y when x = 0.

Thus, from the graph, we have, $b=-7$

Let us substitute the points (-2,7) and (2,-7) in the slope formula,

$m=\frac{-7+7}{2+2}=\frac{0}{4}=0$

Thus, the slope is $m=0$

Substituting the values $m=0$ and $b=-7$ in the formula, we get,

$y=0x-7$

Thus, the linear function of the equation is $y=0x-7$