Question

What is the linear function equation represented by the graph? f(x)=______________

Answer 1

The linear function equation represented by the graph is $\boxed{y = - \frac{1}{2}x + 1}.$

Further explanation:

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

$\boxed{y = mx + c}$

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,

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

Given:

Explanation:

From the graph it has been observed that the line passes through the points $\left( {0,1} \right)$ and $\left( {2,0} \right).$

The line intersect y-axis at $\left( {0,1} \right).$

Therefore, the y-intercept is 1.

The line the line passes through the points $\left( {0,1} \right)$ and $\left( {2,0} \right).$

The slope can be obtained as follows,

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

The slope of the line is $- \dfrac{1}{2}.$

Substitute $- \dfrac{1}{2}$ for m and 1 for c in equation $y = mx + c$ to obtain the equation of the line.

$y = - \dfrac{1}{2}x + 1$

The linear function equation represented by the graph is $\boxed{y = - \frac{1}{2}x + 1}.$

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 inequality, shaded region, y-intercept, graph, representation, origin.

Answer 2

Given the graph shows a clear picture of where the line hits the y-axis, slope-intercept form would make the most sense for describing this line. The slope-intercept form of a line is described by the equation:

y = mx + b

Where m is the slope, b is the y-intercept, and x and y describe a point (x, y) on the line.

We see that the line hits the y-axis at y = 1, so we know that b = 1. To find the slope m, we can look at how x changes for some change in y. We notice that, as x increases by 2, y decreases by 1, so the slope of the graph - the change in y over the change in x - is m = -1/2.

So, the complete equation for our line is

$y=- \frac{1}{2} x+1$

or

$f(x)=- \frac{1}{2}x+1$