Acc. College Algebra- Sec.3.4-3.6-Mangum
Terms
undefined, object
copy deck
-
Definition:
Linear equation in two variables - Any equation that can be written in the form ax+by=c, a,b,c€R and both a,b do not =0
- What is the relationship between the solutions to a linear equation in two variables and the graph on the equation?
- There are an infinite number of solutions, but not any pair will work. Only specific ones will.
- x-intercept
- Where the line crosses the x-axis. The form of the poing will always be (x,0), where x is the crossing point.
- y-intercept
- Where the line crosses the y-axis. The form of the point will always be (0,y) where y is the crossing point.
- Horizontal line
- Can be written in the form y=a, where a€R (no x-intercept)
- Vertical line
- Can be written in the form x=a, where a€R (no y-intercept)
- Line throught the origin
- can be written in the form ax+by=0 where a,b€R. (the x/y-intercept is the same point, specifically the origin)
- Slope
- m=Δy/Δx=y2-y1/x2-x1 where (x1,y1) and (x2,y2) are points on the line
- Four types of slope
-
positive-m>0
negative-m<0
zero slope-m=0, horizontal line
undefined slope, vertical line - Parallel line
- The slopes of the two lines are the same
- Perpendicular lines
- The slopes of two lines are negative reciprocals of each other.
- Forms of linear equations (4)
-
Vertical line
Horizontal line
Standard form
Slope-Intercept form
Point-Slope form - Standard form
- Ax+By=C, A>=0, A,B,C€Z m=-A/B
- Slope-Intercept form
- y=mx+b m=slope, y-intercept (0,b)
- Point-Slope form
- y-yâ‚=m(x-xâ‚) , (xâ‚,yâ‚) is a point on the line, m= slope