 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:

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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

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 (x 1, y 1 ) and slope, m

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

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