Download 06) Linear Equations In Two Variables

06 Linear equations in two variables
A linear equation in two variables is an equation of the form Ax+By=C
where A, B and C are real numbers and A and B cannot both be 0.
of a linear equation is a line.
Graphing a linear equation using the point-plotting method (on page 05)
The best way to graph a line in the standard form Ax+By=C is to find the intercepts.
Graph the equation of a line in standard form Ax+By=C by finding the intercepts.
To find the x-intercept we let y=0.
To find the y-intercept we let x=0.
A vertical line is given by an equation of the form x=a. Where (a,0) is the x-intercept.
Ex. 5) y=-2
A horizontal line is given by an equation of the form y=b. Where (0,b) is the y-intercept
Slope of a given line:
Let P =(x , y ) and Q =(x , y ) be two distinct points. If x does not equal x the slope of a non-vertical line L containing P and Q is defined
by the formula.
Slope = Vertical change (change in y)
Horizontal change (change in x)
Colloquially
=rise/ run
Using 0 in division
finding and intercepting the slope of a line:
When the slope is positive, the line slants up from left to right.
When the slope is negative, the line slants down from left to right.
When the line is horizontal, the slope is zero.
When the line is vertical, the slope is undefined
Find the linear equation of a line given at least one point and the slope
Point slope form of an equation of a line
We use this formula when we know the slope and at least one point on the line.
We should be able to write the equation given 1 point and the slope
Slope intercept form of equation of a line:
Ex. 10.) Find the equation of a line whose slope is 3 and that contains the point (-2,5).
An equation of a line L with slope m and y-intercept b is:
y=mx+b where b is the y-intercept
Ex. 11.) graph x-3y=9 by first converting to slope-intercept form.
Ex. 11.5) graph 2x+3y=6 using slope intercept form.