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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

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

or

[tex]f(x)=- \frac{1}{2}x+1[/tex]

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

Further explanation:

The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.

[tex]\boxed{y = mx + c}[/tex]

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

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

Given:

Explanation:

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

The line intersect y-axis at [tex]\left( {0,1} \right).[/tex]

Therefore, the y-intercept is 1.

The line the line passes through the points [tex]\left( {0,1} \right)[/tex] and [tex]\left( {2,0} \right).[/tex]

The slope can be obtained as follows,

[tex]\begin{aligned}m&=\frac{{0 - 1}}{{2 - 0}}\\&= \frac{{ - 1}}{2}\\\end{aligned}[/tex]

The slope of the line is [tex]- \dfrac{1}{2}.[/tex]

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

[tex]y = - \dfrac{1}{2}x + 1[/tex]

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

Learn more:

  1. Learn more about inverse of the function https://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 https://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.

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