Question

What is the linear function equation represented by the graph?

Answer 1

Answer:

$f(x)=\frac{2}{3}x+3$

Step-by-step explanation:

Let

$A(-3,1), B(0,3)$

Find the slope AB

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{3-1}{0+3}$

$m=\frac{2}{3}$

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

$m=\frac{2}{3}$

$b=3$ -----> the y-coordinate of point B

substitute

$f(x)=\frac{2}{3}x+3$

Answer 2

The linear function is $\boxed{\frac{2}{3}x + 3}$ that represents the given graph.

Further explanation:

Explanation:

The line intersect $\text{y}$-axis at $\left( {0,3} \right).$

Therefore, the $\text{y}$-intercept is 3.

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ can be expressed as,

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

The line the line passes through the points $\left( {0,3} \right)$ and $\left( {-3,1} \right).$

The slope can be obtained as follows,

$\begin{aligned}m&= \frac{{1 - 3}}{{ - 3 - 0}}\\&= \frac{{ - 2}}{{ - 3}}\\&= \frac{2}{3}\\\end{aligned}$

The slope of the line is $\dfrac{2}{3}.$

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

Substitute $\dfrac{2}{3}$ for m and 3 for c in equation $y = mx + c.$

$y = \dfrac{2}{3}x + 3$

The linear function is $\boxed{\frac{2}{3}x + 3}$ that represents the given graph.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: graph function, numbers, slope, slope intercept, equation, linear equation, linear function, y-intercept, graph, representation, origin.