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Question Find the equation of the linear function with yy-intercept (−4)(-4) and xx-intercept (5,0)(5,0). f(x)=45x−4 f(x) = \frac{4}{5}x - 4

Studdy Solution

STEP 1

Assumptions
1. The yy-intercept of the linear function is (0,−4)(0,-4).
2. The xx-intercept of the linear function is (5,0)(5,0).
3. A linear function can be written in the form f(x)=mx+bf(x) = mx + b, where mm is the slope and bb is the yy-intercept.

STEP 2

To find the equation of the linear function, we first need to determine its slope, mm. The slope of a line can be found using the formula:
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two distinct points on the line.

STEP 3

We will use the yy-intercept (0,−4)(0,-4) as point (x1,y1)(x_1, y_1) and the xx-intercept (5,0)(5,0) as point (x2,y2)(x_2, y_2) to calculate the slope.
m=0−(−4)5−0m = \frac{0 - (-4)}{5 - 0}

STEP 4

Simplify the numerator and denominator to find the slope.
m=45m = \frac{4}{5}

STEP 5

Now that we have the slope, we can use the yy-intercept to write the equation of the line. Since the yy-intercept is (0,−4)(0,-4), this means b=−4b = -4.

STEP 6

Substitute the slope mm and the yy-intercept bb into the linear function form f(x)=mx+bf(x) = mx + b.
f(x)=45x−4f(x) = \frac{4}{5}x - 4
This is the equation for the linear function with the given yy-intercept (0,−4)(0,-4) and xx-intercept (5,0)(5,0).

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