Objective To graph horizontal vertical and oblique lines

Objective - To graph horizontal, vertical, and oblique lines using tables of values and intercepts. Linear Equations ? x y = 2 x + 1 -2 -1 0 1 2 3 4 2(-2) + 1 = -3 2(-1) + 1 = -1 2(0) + 1 = 1 2(1) + 1 = 3 2(2) + 1 = 5 2(3) + 1 = 7 2(4) + 1 = 9 y y = 2 x + 1 x This line represents all the solutions to y = 2 x + 1

Linear Equations Non-linear Equations

Write the equation in function form, complete the table, and graph. x -6 -4 -2 0 2

Write the equation in function form, complete the table, and graph. x y -6 -4 -2 0 2 x

Write the equation in function form, make a table, and graph. x -6 -3 0 3 6

Write the equation in function form, complete the table, and graph. x y -6 -3 0 3 6 x

Graphing Using Intercepts Graph x + y = 5 x-intercept (5, 0) y Line is oblique y-intercept (0, 5) x

Finding Intercepts x-intercept = where the line crosses the x-axis y-intercept = where the line crosses the y-axis Oblique y = 2 x + 3 x y -3 -3 -2 -1 -1 1 0 3 1 5 2 7 y x x-intercept (set y = 0) y = 2 x + 3 0 = 2 x + 3 -3 -3 -3 = 2 x 2 2 y-intercept (set x = 0) y = 2 x + 3 y = 2(0) + 3 y=3

Find the x-intercept and y-intercept. x-intercept (Set y = 0) 1) 4 x + 2 y = 6 4 x + 2(0) = 6 4 x = 6 4 4 y-intercept (Set x = 0) 4 x + 2 y = 6 4(0) + 2 y = 6 2 2

Find the x-intercept and y-intercept. 2) 3 x - y = -5 x-intercept (Set y = 0) 3 x - y = -5 3 x - (0) = -5 3 x = -5 3 3 y-intercept (Set x = 0) 3 x - y = -5 3(0) - y = -5 -1(-y = -5)

Graph using the x-intercept and y-intercept. 2 x - 3 y = 8 x-intercept (Set y = 0) 2 x - 3(0) = 8 2 x = 8 x=4 2 2 or (4, 0) y-intercept (Set x = 0) 2(0) - 3 y = 8 -3 -3 y x

Graph using the x-intercept and y-intercept. 3 x + 5 y = 150 x-intercept (Set y = 0) 3 x + 5(0) = 150 y 40 3 x = 150 x = 50 30 3 3 20 or (50, 0) 10 y-intercept (Set x = 0) -50 -40 -30 -20 -10 3(0) + 5 y = 150 -10 -20 5 y = 150 -30 5 5 -40 0 10 20 30 40 50 x

Types of Lines Oblique Equation Ax + By = C form Horizontal Vertical y=k Example 3 x - 2 y = 5 y = -7 Universal constants A=3 B = -2 C=5 k = -7 x=k A, B and C are integers (no fractions or decimals). k represents a rational number.

Graphing Horizontal and Vertical Lines x y -2 7 -1 6 0 5 1 4 2 3 3 2 4 1 5 0 6 -1 Graph x + y = 5 y Line is oblique x

x y -2 -2 -2 -1 0 1 2 3 4 5 Graph. x = -2 Line is Vertical y x Any line in the form x = k will be vertical.

x y -2 -1 0 1 2 3 4 5 3 3 3 3 Graph. y=3 Line is Horizontal y x Any line in the form y = k will be horizontal.

Review Horizontal Line Vertical Line y=k x=k Perpendicular to y-axis. Perpendicular to x-axis.

A) Graph x = -4 on a number line. -5 -4 -3 -2 -1 0 1 2 3 B) Graph x = -4 on a coordinate plane. y x

Finding Intercepts x-intercept = where the line crosses the x-axis y-intercept = where the line crosses the y-axis Horizontal y = 2 x-int. = none y y-int. = 2 x Vertical x = -1 x-int. = -1 y-int. = none y x

Find the x-intercept and y-intercept. 1) x = 5 x-intercept x = 5 or (5, 0) 2) none 3) x = -1 (-1, 0) y-intercept none

Find the x-intercept and y-intercept. 4) x = -3 x-intercept x = -3 or (-3, 0) 5) none 6) x = 0 (0, 0) y-intercept none y-axis