Mathematics: PLEASE HELP!! Consider the function shown on the graph. Complete the statements to make them true. This is the graph of a____ function. The x-intercept of the function is at____

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PLEASE HELP!! Consider the function shown on the

Jasten

13.02.2022

This is the graph of a linear function.

The x-intercept of the function is at (8,0)

Step-by-step explanation:

Given

The attachment

Required

Fill in the gaps

Function Type

From the attachment, it can be observed that the graph represents a linear function. See proof below

Take any 3 points of x and y

(x_1,y_1) = (8,0)

(x_2,y_2) = (0,-2)

(x_3,y_3) = (4,-1)

Calculate the slope:

$m = \frac{y_3 - y_2}{x_3 - x_2}= \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-1 - (-2)}{4 - 0}= \frac{-2 - 0}{0 - 8}$

$m = \frac{-1 +2}{4}= \frac{-2}{- 8}$

$m = \frac{1}{4}= \frac{2}{8}$

$m = \frac{1}{4}= \frac{1}{4}$

Notice that the slope is consistent for the three coordinate points.

Hence, the graph is a linear function

x intercept

This is the point where y = 0

From the graph;

x = 8 when y = 0

Hence, the x intercept is 8

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