Geometry Notes 10/6+10/7

Linear Equations

Linear Equation- An Equation that represents a line graph. Ex. y=mx+b
Slope- The steepness or flatness of a line as well as its direction.
Y-intercept- where your graph crosses the y- axis
X-intercept- where your graph crosses the x- axis
Parallel lines- Lines that never intersect have the same slope or the same m.
Perpendicular lines- lines that form a 90 degree angle upon intersection. Their slopes are negative, reciprocals of each other. Ex. If one slope is 3 then the line perpendicular to it is – 1/3

y=mx+b

This is the slope-intercept form for the equation of a line, it shows what the slope is and what the y-intercept is.
M= the slope of the line. RISE OVER RUN
B= the y- intercept
x and y are any point on your graph.
When you write an equation you do not include the x and y because they can be multiple points
Ex. Y=3x+7, slope = 3 or 3 over 1, y-intercept = 7

Graphing a Line using slope-intercept form

When graphing a line you only need two points.
Make sure your equation is in y=mx+b form
Plot a point on your b, that is your y-intercept. This is your 1st Point.
From your y-intercept, use your slope to graph the next point. Rise (if m is positive) or Drop (if m is negative) then run to the right. Plot your next point at that spot. Ex. 3/2 is the slope. Rise 3, run to the right 2, then plot your point.
Finally draw a line through your two points, with arrows at each end