2.3 – slopes, forms of lines. slope slope = measure of steepness of a line in the cartesian plane...
TRANSCRIPT
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