Question

The functionf (x)is shown in the graph.

Answer 1

After finding the intercept form of the graph of the given straight line, it can be obtained that $f(x)=-\frac{4}{5}x-3$.

How to find the equation of a straight line in intercept form from its graph?

If the graph of a straight line cuts the x-axis at the point $(a,0)$ and the y-axis at the point $(0,b)$, then the equation of the straight line in intercept form will be $\frac{x}{a}+\frac{y}{b}=1$.

Here, in the given figure, we can see that the graph of $y=f(x)$ is a straight line.

From the graph, we can see that the straight line cuts the x-axis at the point $(-3\frac{3}{4},0)=(-\frac{15}{4},0)$ and cuts the y-axis at the point $(0,-3)$.

So, here, $a=-\frac{15}{4}$ and $b=-3$.

Hence, the equation of the straight line in intercept form is

$\frac{x}{a}+\frac{y}{b}=1\\\frac{x}{-\frac{15}{4}}+\frac{y}{-3}=1\\\frac{y}{-3}=1+\frac{4x}{15}\\y=-\frac{4}{5}x-3$

Therefore, finding the intercept form of the given straight line, we obtain that $f(x)=-\frac{4}{5}x-3$.

To learn more about intercept form, refer: brainly.com/question/20385214

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Answer 2

$f(x)=-\frac{3}{4}x-3$

What is a graph?

A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. 5. A mathematical function or equation is shown by a curve or line, usually represented using a Cartesian coordinate system.

The equation for f (x):

$y=f(x)=mx+b$

The slope of the line is m.

The point of intersection of the line with the y-axis is b.

To find the slope first by the following formula:

$=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

Two points of the line: $(x_{1} ,y_{1})=(x_{2},y_{2} )$

$(x_{1} ,y_{1})=(-4,0)$

$(x_{2} ,y_{2})=(0,-3)$

Substituting:

$m=\frac{-3-0}{0-(-4)}$

$m=-\frac{3}{4}$

Find the y-intercept Looking at the graph, we find the line intercepts the y-axis at y=-3.

Therefore, b=-3.

To learn more about graphs, refer to:

brainly.com/question/11440676

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