What is the linear function equation represented by the graph?

Graph of a line on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. A line intersects the y-axis at begin ordered pair 0 comma negative 4 end ordered pair and passes through at begin ordered pair 3 comma negative 3 end ordered pair.

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f(x)=

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akposevictor akposevictor · Answer 1 · 2020-12-16T04:58:41+01:00

Answer:

[tex] f(x) = \frac{1}{3}x - 4 [/tex]

Step-by-step explanation:

The linear function equation that could represented by the graph can be written in the slope-intercept form, as [tex] f(x) = mx + b [/tex]

Where,

m = slope of the graph = rise/run

b = y-intercept = the point where the line intercepts the y-axis. At this point, x = 0.

Let us find the values of m and b respectively.

Using two points, (3, -3) and (0, -4),

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{0 - 3} = \frac{-1}{-3} = \frac{1}{3} [/tex]

m = ⅓.

The y-axis is intercepted at y = -4, when x = 0.

Therefore,

b = -4 (y-intercept)

Substitute b = -4, and m = ⅓ into [tex] f(x) = mx + b [/tex]

The linear function equation would be:

[tex] f(x) = \frac{1}{3}x + (-4) [/tex]

[tex] f(x) = \frac{1}{3}x - 4 [/tex]