Chapter 3
Equation in linear form
Ax + By = C
Finding horizontal/vertical lines
Horizontal=y Vertical=x`
Vertical Line Test
If a vertical line can be drawn so that it intersects a graph more than once, the graph is not the graph of a function.
Graphing intercepts
Make a table for equations where x=0 and y=0 Plug in 0's to get intercept
Slope-intercept form
When a linear equation in two variables is written in slope-intercept form, y = mx + b ^ ^ slope (0,b), y-intercept then m is the slope of the line and (0,b) is the y-intercept of the line
Find equation of line given 2 points
1.) Find slope Y2 - Y1 -------- = Slope X2 - X1 2.) Point Slope Form Y - Y1 = M(X - X1)-
Find slope given two points
1: Change in y ------------ Change in x 2. Y2- Y1 ------- = m X2- X1
Function
A function is a set of ordered pairs that assigns to each x value exactly one y value. IN OTHER WORDS A FUNCTION CANNOT HAVE TWO ORDERED PAIRS WITH THE SAME X COORDINATE BUT DIFFERENT Y COORDINATES.
Parallel and Perpendicular lines
Non-vertical parallel lines have the same slope The product of the slopes of two non-vertical perpendicular lines is -1
Parallel lines
Non-vertical parallel lines have the same slope and different y-intercepts
Summary of Slope
Slope m of the line through (x1, y1) and (x2, y2) is given by the equation . y2 - y1 m = ----------- x2 - x1
Horizontal Lines
The Graph of y=c, where c is a real number, is a horizontal line with y-intercept (0,c)
Point Slope Form of the equation of a line
The POINT-SLOPE FORM of the equation of a line is y - y1 = m ( x - x1) ^-----|----------^(x1,y1) point on the line slope where m is the slope of the line and (x1,y1) is a point on the line.
Slope of a Line
The slope m of the line containing the points (x1,y1) and (x2,y2)is given by Rise Change in y y2 - y1 m=------ = ------------------- = ----------- as long as x2 ≠ x1 Run Change in x x2 - x1
Vertical line through (-1,5)
X=-1
Slope intercept form
Y = mx + b --- -- Slope Y-intercept
Extras
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Find slope on line given two points
Y2 - Y1 -------- = Slope X2 - X1
Forms of linear equations
Ax + By = C |Standard form of a linear equation. | A and B are not both 0 -------------------------|------------------------------------------------------ y = mx + b |Slope intercept form of a linear |equation.The slope is m and the |y-intercept is (0,b). ------------------------ |------------------------------------------------------ y - y1 = m(x - x1) |Point slope form of a linear equation. |The slope is m and (x1,y1) is a point . . |on the line. -------------------------|------------------------------------------------------ y=c |Horizontal line | The slope is 0 and the y-intercept is . . |(0,c). -------------------------|------------------------------------------------------ x=c | Vertical line |The slope is undefined and the |x-intercept is (c,0)
Perpendicular lines
If the product of the slopes of two lines is -1, then the lines are perpendicular. (Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.)
Finding perpendicular lines
Know if when slopes are multiplied they equal -1
X and Y intercept
On the X or Y axis. X=0 or Y=0 (0,7) (5,0) ^ ^ Y-intercept X-intercept
Vertical Lines
The graph of x=c where c is a real number, is a vertical line with x-intercept (c,0)
Finding x and y intercepts
To find the x-intercept, let y=0 and solve for x To find the y-intercept let x=0 and solve for y
Slope-Intercept Form
When a linear equation in two variables is written in slope-intercept form, y=mx+b m is the slope of the line and (0,b) is the y-intercept of the line
Find equation of a line given slope and a point
Y - Y1=M(x - X1)
Horizontal line passing through (3,-2)
Y=-2