Question

Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay.

Answer 1

linear decreasing

Explanation:

Given,

There is a straight line in the graph,

We know that a straight line is always shows a linear function,

Now, the line is passes through the points (-3.5, 0) and (0, -5),

Since, the slope of a line passes through
`(x_1, y_1)` and
`(x_2, y_2)` is,

`m=(y_2-y_1)/(x_2-x_1)`

So, the slope of the linear function in the graph,

`m=(-5-0)/(0+3.5)=(-5)/(3.5)=-(10)/(7)`

A linear function with the negative slope is always called linear decreasing function.

Hence, the graph represents linear decreasing.

Answer 2

Answer with explanation:

Taking to points on the linear function ,that is x intercept and y intercept which are, (-2.5,0) and (0,-5) and writing the equation of line

which is given by intercept form

`(x)/(a)+(y)/(b)=1`

`(x)/(-2.5)+(y)/(-5)=1\\\\ (2x)/(-5)+(y)/(-5)=1\\\\ 2 x +y=-5`

y = -5 - 2 x

Taking y as a dependent variable ,and x as as independent variable

x -1 0 1 2 3 4

y -3 -5 -7 -9 -11 -13

with increase in x value ,y value decreases or vice versa.

that is , if
`x_(1)>x_(2) {\text{but}} y_(1) < y_(2)`

then it is a decreasing function.

So, the given function is linear decreasing function.

Option B: Linear Decreasing