Download MAT 1033 - Review Section 3 Graphing Linear Functions

MAT 1033 - Review Section 3
Graphing Linear Functions
A linear function is a function with no exponents, no variables in the denominator, and no
special symbols. To "solve" a LINEAR FUNCTION, make a graph. The line represents the
solution. Linear functions can be graphed using any of the following techniques.
A. Make a chart and determine at least two ordered pairs. Then plot the points and connect.
1.)
y = 5x – 3
2) y =
2
x−3
3
B. When a linear equation is in Standard Form Ax + By = C it is helpful to graph using the x and y
intercepts. To find the x-intercept substitute 0 for y. To find the y-intercept substitute 0 for x.
Determine the x and y intercepts of the following linear equations and graph the solution.
Ex 1: 2x - 3y = 12
Ex 2: 5x + 2y = 8
x-intercept:
x-intercept:
y-intercept:
y-intercept:
C. When a linear equation is in the Slope-intercept Form - y = mx + b – it is useful to graph using
the y-intercept as your first point and the slope (rise over run) to determine additional point(s).
Identify the slope and y-intercept for each function and then graph.
1
x-2
2
Ex 2. y = -3x + 4
Ex 3. y = -x - 1
Slope:
Slope:
Slope:
y-intercpet:
y-intercept:
y-intercept:
Ex 1. y =
D. When a linear equation is in any other form, it is often useful to solve the equation for y, then
graph using the slope and y-intercept. Solve the following equations for y, identify the slope
and y-intercept, then graph the solution.
Ex 1. 3y = 4x + 12
Solve for y:
Ex 2. 8 + 2y = 6x
Slope:
y-intercpet:
Slope:
y-intercept:
Ex 3. 5x – 2y = 10
Slope:
y-intercept:
(Note: You would then graph these equations as those in section C.)
E. Review of vocabulary:
1. The slope can be described as _____________.
2. The slope-intercept form of the equation of a line is
where _____ is the slope, and _____ is the y-intercept.
3. The standard form of the equation of a line is: ________________.
4. To find the x-intercept substitute ____ for ____ and solve.
5. To find the y-intercept substitute ____ for ____ and solve.
F. Review of "methods" for solving:
1. Linear equation:
Method:
3(x – 1) + 2 = 5x – 6
2. Polynomial (quadratic) equation:
Method:
3. Rational equation:
x2 – 7x = 8
1 3 7
− =
x 5 2
Method:
4. Linear function:
Method:
3x – 8 = 2y
HW: Section R3 Page 943 – Problems 13-16,21-24
Hint: When asked for the slope and/or y-intercept, solve for y first.
Section 3.3 Page 159 – Problems 17 – 24 all
Review HW: Pg 406 Problems 9, 10, 13, 23
(022)