Respuesta :

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

[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]

[tex]\frac{x}{-2.5}+\frac{y}{-5}=1\\\\ \frac{2x}{-5}+\frac{y}{-5}=1\\\\ 2 x +y=-5[/tex]

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 [tex]x_{1}>x_{2} {\text{but}} y_{1} < y_{2}[/tex]

then it is a decreasing function.

So, the given function is linear decreasing function.

Option B: Linear Decreasing

Answer:

linear decreasing

Step-by-step 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 [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]m=\frac{-5-0}{0+3.5}=\frac{-5}{3.5}=-\frac{10}{7}[/tex]

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

Hence, the graph represents linear decreasing.

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