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DA Algebra 1-1 4.4 Notes 2016
X & Y Intercept and Parallel & Perpendicular Lines Notes
Objective: You will be able to graph a linear equation from SIF, PSF, and Standard Form using x and
y-intercepts. You will understand parallel and perpendicular lines.
The graph of the linear equation 2x + 3y = 6 is displayed below. Write the ordered pairs representing
the x and y intercepts on the graph.
The x-intercept is the value of x when y = 0.
x-intercept ___________
The y-intercept is the value of y when x = 0
y-intercept _______________
Confirming/Finding x and y intercept algebraically.
To find the x-intercept:
To find the y-intercept:
Write the original equation:
Write the original equation:
Substitute 0 for y:
Substitute 0 for x:
Solve for y:
Solve for x:
The x-intercept is ___________
The y-intercept is ___________
The line crosses the x-axis at the point ______
The line crosses the y-axis at the point ______
Graph the equation -3x + 6y = 18 by making a quick graph using the x and y intercepts.
Step 1: Find the x-intercept:
Step 2: Find the y-intercept
To find the x-intercept:
To find the y-intercept:
Write the original equation:
Write the original equation:
Substitute 0 for y:
Substitute 0 for x:
Solve for x:
Solve for y:
The y-intercept is _________
The x-intercept is _________
The line crosses the y-axis at the point ______
The line crosses the x-axis at the point ______
Step 3: Plot and label the x-intercept and the y-intercept
Step 4: Draw a line connecting the x and the y intercepts.
Step 5: Label the line.
Practice: Graph using x and y intercepts.
5 x  3 y  15
Practice: Find the x and y-intercept of the line. Graph the equation.
1.) y = -6 + 3x
2.) -x + y = -3
3.) 4x + 5y = 20
4.) -y = -2x – 4
Part 2: Algebraically Practice Finding the X and Y Intercept
Algebraically Find the x and y-intercepts.
Remember: For the x-intercept, find the value of x, therefore substitute 0 for y and solve.
For the y-intercept, find the value of y, therefore substitute 0 for x and solve.
a. 2x + y = 6
b. 4x + 8y = -32
c. y = x + 5
x-intercept: ________
x-intercept: ________
x-intercept: ________
y-intercept: ________
y-intercept: ________
y-intercept: ________
Practice
d. y = -8 – 2x
e. -4x + 16y = -16
x-intercept: ________
x-intercept: ________
x-intercept: ________
y-intercept: ________
y-intercept: ________
y-intercept: ________
f. y =
1
x + 10
2
PART 3: X & Y-Intercept application
1. To raise money for a charity, your club is selling flowers and candy on Valentine’s day. Each rose cost
$2.50 and a box of candy cost $10. Your club made a total of $340 for charity.
a) Write an equation in Standard Form (Ax + By = C) representing this situation. Let x be the number of flowers
and y be the number of candy boxes.
b) Identify and interpret the x-intercept.
c) Identify and interpret the y-intercept.
2. The graph below shows the relationship between the
number of days and the pages left to write an English paper.
a) Identify and interpret the slope
b) Identify and interpret the x-intercept
c) Identify and interpret the y-intercept
PART 4: Parallel and Perpendicular Lines
Example 1: Parallel and Perpendicular Lines
A. Find the slope of lines a and b.
B Find the slope of lines c and d.
Line a: ______ Line b: ______
Line c: _________ Line d: ________
Lines are parallel if
Lines are perpendicular if
Partner Practice: Identifying/graphing parallel and perpendicular lines.
Rewrite each equation in SIF and graph. Label your lines.
A. –x + 2y = 6
B. –x + 2y = -2
C. 2x + y = 4
Example 2:
1) For lines to be parallel, what must be true about their slopes?_________________________
2) Give an example of two slopes that are parallel. _________________
3) For lines to be perpendicular, what must be true about their slopes?__________________________
4) Give an example of two slopes that are perpendicular. __________________
5) What form must an equation be in for you to know the slope? _________________________
6) What is always true about the slopes of horizontal (y = #) and vertical (x = #) lines?
_______________________________________________________________________
7) Write the equation of a line that is perpendicular to
y = 2 _______________
(hint: it may help if you graph the line)
Practice
1) Are these lines parallel, perpendicular, or neither? (Get equations in slope intercept form first.
Then circle the slopes). Justify your answer.
a) y = -6x +2
b) y = 9x – 3
c) y = 2x + 3
y = -6x
-1/9 x + 2 = y
y = 7 – 2x