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Math  /  Algebra

QuestionFind the equation of the linear function f(x)f(x) such that f(−2)=−6f(-2)=-6 and f(−1)=6f(-1)=6. Submit your answer in slopeintercept form.

Studdy Solution

STEP 1

1. We are given two points on the line: (−2,−6)(-2, -6) and (−1,6)(-1, 6).
2. The equation of the line is to be found in slope-intercept form, y=mx+by = mx + b.
3. We need to calculate the slope mm and the y-intercept bb.

STEP 2

1. Calculate the slope mm of the line.
2. Use the slope and one of the points to find the y-intercept bb.
3. Write the equation in slope-intercept form.

STEP 3

Calculate the slope mm using the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (−2,−6)(-2, -6) and (−1,6)(-1, 6):
m=6−(−6)−1−(−2) m = \frac{6 - (-6)}{-1 - (-2)}

STEP 4

Simplify the expression to find the slope:
m=6+6−1+2=121=12 m = \frac{6 + 6}{-1 + 2} = \frac{12}{1} = 12

STEP 5

Use the slope m=12m = 12 and one of the points, say (−2,−6)(-2, -6), to find the y-intercept bb using the equation y=mx+by = mx + b.
Substitute x=−2x = -2, y=−6y = -6, and m=12m = 12 into the equation:
−6=12(−2)+b -6 = 12(-2) + b

STEP 6

Solve for bb:
−6=−24+b -6 = -24 + b
Add 24 to both sides:
b=18 b = 18

STEP 7

Write the equation of the line in slope-intercept form using the slope m=12m = 12 and y-intercept b=18b = 18:
y=12x+18 y = 12x + 18
The equation of the linear function is:
f(x)=12x+18 f(x) = 12x + 18

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