Point Slope, Intercept method
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
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