Point Slope, Intercept method

Topics: Slope, Linear equation, Analytic geometry Pages: 6 (1218 words) Published: October 28, 2014
Algebra II Test Study Guide

Will H. and Blaine S.

The Intercept Method:
-The x-intercept of a line is the point where a line crosses the x-axis. Its coordinates are (#,0). -The y-intercept of a line is the point where a line crosses the y-axis. Its coordinates are (0,#). 1- Find the x-intercept by letting y=0.

2- Find the y-intercept by letting x=0.
3- Plot the intercepts and graph the line. (If the x and y intercepts are both 0, use a table to find the second point.)
Ex:
x-int:

5x-3y=-30
y=0
5x-3(0)=-30
5x=-30
–– ––
5
5
x= -6 (-6,0)

y-int:

x=0
5(0)-3y=-30
–– ––
-3 -3
y=10 (0,10)

The Slope-Intercept Method:
- The Slope-Intercept form of a line is y=mx+b, where b is the y-intercept ( a point ) and m is the slope.
- Slope is a quotient of two numbers.
∆=“delta”(change)

Slope Definition:

m= Rise
––––
Run

∆y
y 2 - y1
––– = –––––––
∆x
x 2 - x1

1- Solve for y to put the equation in slope intercept form.
2- Plot the y-intercept.
3- Using the slope as a fraction, rise y and run x to get second point. 4- Graph the line.
Ex:

2x+3y=12
-2x
-2x
–––––––––
3y=-2x+12
–– ––––
3
3
y= -2/3x+4
m= -2/3 b= 4

Horizontal and Vertical Lines:
- A Horizontal Line has the form y=#. (In an equation of a horizontal line, there is no x) - The slope of a horizontal line is 0. Picture:
(can walk on the line)

- A Vertical Line has the form x=#. (In an equation of a vertical line, there is no y.) - The slope of a vertical line is undefined. Picture:
(falls off line)
- (*y-intercept = none parallel to y-axis unless x=0)
1- If y is the only variable, solve for y.
2- Draw a horizontal line that crosses the y-axis at what y equals. OR
1- If x is the only variable, solve for x.
2- Draw a vertical line that crosses the x-axis at what x equals. Ex:

Graph y=-3 and 2x-1=3
(Horizontal ^)
+1 +1
2x=4
–– ––
2 2
x=2
(Vertical ^)

Extra:
Point Slope Formula: y-y1=m(x-x1)
Standard Formula: Ax+By=C

Equations of Linear Functions from their Graphs (3.4)
Review formulas from 3.1-3.3
Slope Intercept form is y=mx+b where “m” represents the slope and “b” represents the yintercept • y-intercept - a function is the value of y when x=0
• x-intercept - a function is a value of x when y=0

Slop formula is rise over run, where

y = # is a graph of a horizontal line with a slope equal to 0

x = # is a graph of a vertical line with a slope equal to undefined

Point slope form is y — y1 = m(x — x1), where “m” represents the slope and —y1, —x1 represents the point
Standard form is Ax + Bx = C
Suppose someone says, “If the equation is y = 3x — 8, what are the slope and y-intercept? Slope is 3 and y-intercept is —8
If the slope and y-intercept are —5 and 13, what is the equation? y = —5x+13 In this section you will use information about the graph to write equations of particular liner functions
Objective: Given the information about the graph of a liner function write its particular equation
Example 1: Find the particular equation of the linear function with the slope —3/2, containing the point (7, —5)
Since the point and slope are given the easiest form to use is the point slope form. You would write: y + 5 = —3/2(x—7)
Example 2: Find the particular equation of the linear function containing the points (—4/5) and (6,10)
First using the slope formula to find the slope, m
10 — 5
—5
m = —————— = ———— = 0.5
6+4
10
You can use either of the given points in the point slope form y—5 = 0.5(x+4) or y—10 = 0.5(x—6)
Distribute and simplify both equations above into slope intercept form y — 5 = 0.5x + 2
y — 10 = 0.5x — 3
y= 0.5x + 7
or y = 0.5x + 7
Two lines are parallel to each other if their slopes are equal. Two lines are perpendicular to each other the slope of one is the opposite of the reciprocal of the other
Parallel and Perpendicular Lines
If the equation of a line is y = mx + b, then:

A parallel line also has slope “m”
A perpendicular line has a slope —1/m...
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