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Math  /  Algebra

QuestionFind the equation of the linear function such that f(0)=4f(0)=4 and f(7)=−5f(7)=-5. Submit your answer in slopeintercept form, or y=mx+by=m x+b.

Studdy Solution

STEP 1

1. We are given two points on the line: (0,4) (0, 4) and (7,−5) (7, -5) .
2. We need to find the slope-intercept form of the line, which is y=mx+b y = mx + b .

STEP 2

1. Calculate the slope m m of the line using the two given points.
2. Use the slope and one of the points to find the y-intercept b b .
3. Write the equation of the line in slope-intercept form.

STEP 3

Calculate the slope m m using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (0,4) (0, 4) and (7,−5) (7, -5) :
m=−5−47−0=−97 m = \frac{-5 - 4}{7 - 0} = \frac{-9}{7}
The slope m m is −97 -\frac{9}{7} .

STEP 4

Use the slope m=−97 m = -\frac{9}{7} and the point (0,4) (0, 4) to find the y-intercept b b .
Since f(0)=4 f(0) = 4 , we know that b=4 b = 4 .

STEP 5

Write the equation of the line in slope-intercept form y=mx+b y = mx + b .
Substitute m=−97 m = -\frac{9}{7} and b=4 b = 4 :
y=−97x+4 y = -\frac{9}{7}x + 4
This is the equation of the linear function.

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