Cupcake House

Linear Function
:(Module):

Sharmaine N. Sayao Mathematics
IV-A Mrs. Imelda Sayao

1.1 Definition of a Linear Function

A linear function is a function whose graph is a straight line. The equation of a linear function of x can be written in the form f(x) = mx + b or a linear equation y = mx + b where m is the slope and b is the y-intercept.

The equation in the form Ax + By = C where A, B and C are real numbers is referred to as the general form of a linear equation. We can rewrite a given linear equation Ax + By = C in the form y = mx + b and vice-versa using the basic properties of real numbers and the properties of equality.

EXAMPLE: 1. Rewrite the following linear functions is the form y = mx + b. a. 5x + y = 12
Solution : 5x + 7 = 12 Y = -5x + 12 2. Rewrite the following linear functions in the form Ax + By = C. a. y = 3x – 2
Solution : y = 3x – 2 -3x + y = -2
Or 3x – y + 2

EXERCISES: A. Transform the following linear functions into the form y = mx + b. 1. 2. x + y = 13 6. 2x + 3y = 6 3. -2x + y = 6 7. -4x + 7y = 21 4. 3y – 12x = 0 8. 5x – 4y = 20 5. 5x – y – 2 = 0 9. 3x – 2y = 12 6. x + 7y + 14 = 0 10. -5x – 10y = 30

B. Transform the following linear functions into the form Ax + By = C. 1. y = 2x + 1 6. y = 3x + 4 2. y = -x -4 7. y = -2x + 8 3. y + 2 =x 8. 3x + y – 1 = 0 4. x = -y -6 9. 2x – y +3 = 0 5. 2x – y – 7 = 0 10. y = -3x + 3

C. Determine the value of m and b in the following linear functions. 1. 2(x – 1) = 3y 6. 3(x + 2) = 2y 2. 5x = 4(y – 1) 7. 2x = 3(y – 2) 3. 3(2x + 1) -5y = 1 8. 2(x + 1) -3y = 2 4. 7(x + 2) = 14(y -1) 9. 2(x – 4) = 12(y +3) 5. 30x – 5(y+4) =0 10. 15x + 3(y – 5) = 0

1.2 Slope and Intercepts

The slope is the number that indicates the steepness of a line. The slope is the ratio of the change in y–coordinates the corresponding change in the