Question

What is the linear function equation represented by the graph?

Answer 1

Two points on this line are (0,-4) and (3,-3)
The slope is 1/3 since we go up 1 and over to the right 3 units (when we go from (0,-4) to (3,-3))

We can see this using the slope formula
m = (y2 - y1)/(x2 - x1)
m = (-3 - (-4))/(3 - 0)
m = (-3 + 4)/(3 - 0)
m = 1/3

The y intercept is -4 as this is the location where the graph crosses the y axis.
So b = -4

Plug m = 1/3 and b = -4 into the equation y = mx+b

Doing so leads to the answer of y = (1/3)x - 4
Which is the same as f(x) = (1/3)x - 4

Answer 2

The linear function equation is $\boxed{y = \frac{1}{3}x - 4}.$

Further explanation:

The formula for slope of line can be expressed as,

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

Explanation:

The line intersect $\text{y}$-axis at $\left( {0,- 4} \right).$

Therefore, the $\text{y}$-intercept is -4.

The line passes through the points $\left( {0,- 4} \right)$ and $\left( {3,- 3} \right)$.

The slope can be obtained as follows,

$\begin{aligned}m &= \frac{{- 3 - \left( { - 4} \right)}}{{3 - 0}}\\&= \frac{{ - 3 + 4}}{3}\\&= \frac{1}{3}\\\end{aligned}$

The slope of the line is $\dfrac{1}{3}.$

The slope intercept form of the linear equation is given as follows.

$\boxed{y = mx + k}$

Substitute $\dfrac{1}{3}$ for m and -4 for k in equation $y = mx + k.$

$y = \dfrac{1}{3}x - 4$

The linear function equation is $\boxed{y = \frac{1}{3}x - 4}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

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