Slope and y-intercept
Lines have both slope (m) and a y-intercept (b). Slope describes the steepness of the line as well as its direction. Positive slope means the lines go up toward the right; negative slope means it goes down to the right. The larger the slope, the steeper the line. A slope of 5 is a very steep line, while a slope of 1/5 is very flat. The y-intercept tells you where the line crosses the y- axis. Lines
Slope
You only get better when you practice, so….. Find the slope of the line that passes through the points: 1. (4,4) and (6,6)2. (3,7) and (4,8) m = 1 m = 1 3. (7,-5) and (-4,-4)4. (-6,-1) and (7,-6) m = -1/11 m = -5/13 Slope
Slope tells you how to move and the y-intercept tells you where the line cross the y-axis. y = mx + b……you have seen this before m is the slope and b is the y-intercept. When giving the y-intercept, give the coordinates as an ordered pair. (0,b) You can use those two things to graph any line. y = 2x + 3 Slope is 2 and the y-intercept is (0,3). Slope - Intercept
Try a couple more……. 1. y = 5x – 62. y = -2x + 3 3. y = -1/3x y = 1/2x - 4 Slope-Intercept
Now we will practice writing equations. Remember you have to have a slope (m) and a y- intercept (b) to write an equation. Write the equation for the line given the slope and intercept. 1. m = 2 y-intercept (0,5) 2. m = -8 y-intercept (0,4) 3. m = ½ y-intercept (0,-3) Slope-Intercept 1.y = 2x y = -8x y = 1/2x - 3
Now for the hard ones…… What happens if you have the slope, but not the y- intercept? Solve for it!!! Write the equation of the line that has a slope of 2 and passes through (4,6). y = mx + b 6 = 2(4) + b 6 = 8 + b b = -2 y = 2x - 2 Slope-Intercept Plug in the numbers that you know: m = 2, y = 6, x = 4 Solve for b. Rewrite in slope-intercept form.
I know, that was tricky so try it again…. m = 4 (-1,2) 2 = 4(-1) + b 2 = -4 + b b = 6 y = 4x + 6 Slope-Intercept m = -1/2 (4,-6) -6 = -1/2(4) + b -6 = -2 + b b = -4 y = -1/2x - 4