2.3 – Slopes, Forms of Lines

Slope

• Slope = measure of steepness of a line in the Cartesian plane for two points

• Slope = m =

• Two ways to calculate slope:– 1) Plot the line, count Rise and Run– 2) Use the slope formula

12

12

xx

yy

Run

Rise

2211 ,,, yxyx

• Example. Find the slope between the two points:

• A) (-4,-3) and (2,-5)

• B) (-2,7) and (1,7)

Horizontal, Vertical

• Horizontal Lines = no change in the rise, so m = …

• Vertical Lines = no change in the run, so m = …

Forms of Linear Equations

• Using the idea of slope, we can write different forms of linear equations

• Each will allow us to graph without using a table OR graphing utility (boo!)

Slope-Intercept

• The Slope-Intercept form of a linear equation: y = mx + b– m = slope– b = y-intercept

• To graph an equation in this form, we can:– 1) Use y-intercept as a starting point– 2) Use the slope to find 2 other points

• Ex. Graph the equation 4x – 4y = 16.• Solve for y, first!

Point-Slope Form

• On the other hand, if we do not know a y-intercept, we can use Point-Slope form of an equation: – Using the point (x1, y1) and slope, m

)( 11 xxmyy

• Example. Find the equation, in point-slope form, of the line passing through the points (-3,-2) and (1,6).

• Can we find the slope?

• Example. Using the information from the previous problem, find the slope-intercept form of the equation.

• Assignment• Pg. 154• 1-7 odd, 13-19 odd, 25, 29, 31, 35, 37, 41, 45,

47-50