Slope and Equations of Lines Reviewing types of slope Remember, there are four types of slope: Positive Negative No slope Undefined slope The slope of a line
The slope of a nonvertical line passing thru the points (x1,y1) (x2,y2) : y2 y1 rise m x2 x1 run Find the slope of a line passing thru (-3,5) &
(2,1) 1 5 4 4 m 2 ( 3) 2 3 5 W/out graphing, tell whether the line thru the points is positive, negative, horizontal, or vertical. 1) m>0, positive slope
(3,-4), (1,-6) 6 ( 4) 6 4 2 m 1 1 3 2 2 Undefined: 2) (2,-1), (2,5) The line is 5 ( 1) 5 1 6
m vertical 2 2 0 0 What is the slope of the line? 2x y 3 2x y ( 2x) ( 2x) 3 y 2x 3 The constant, b = 3 is the y-intercept.
The coefficient, m = -2 is the slope. Fill in the Blank Parallel Lines have the _______ slope. Perpendicular Lines have slopes that are _________ __________. Ex: y = 3x - 6
A. y = 2x + 1 B. y = 3x + 4 C. y = -3x + 6 D. y=
Which equation is parallel? Which equation is perpendicular? Ex: 4x 8y = -16 A. y = 2x + 4 B. y = -2x - 1 C.
y = -x - 3 D. y= Which equation is parallel? Which equation is perpendicular? Ex : Tell whether the lines are ,, or neither L1: thru (-3,3) & (3,-1)
L2: thru (-2,-3) & (2,3) 1 3 4 4 2 l1m1 3 ( 3) 3 3 6 3 3 ( 3) 3 3 6 3
l2 m2 2 ( 2) 2 2 4 2 Negative reciprocals Of each other : They are . Equation of a Line What is slope-intercept form? Slope-Intercept Form
Find the slope of the line y = 2x - 4. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 y = 2x - 4 2 4 6 8
rise slope 2 run The y-intercept is -4. y 2x 1 right 1 right 1 up 2 up 2 Example: Graph 3x + 4y = 12 y
Step 1: Put equation in slope intercept form x Example Write the equation of the line with slope = -2 and passing x1 , y1 ) through the point (3, (-5).
Substitute m and substitute Form. into the Slope Intercept Y=-2x+b -5=-2(3)+b 1=b
Y=-2x+1 Ex : Write the equation of the line with m=3 and through the point (2,-3) Y=mx+b Y=3x+b -3=3(2)+b -9=b Write the Equation for the line:
Through (-2,1) and parallel to y=-3x+1 Plug the point (-2,1) into the equation y=mx+b 1=m(-2)+b If it is parallel, then they have the same slope! So m=-3 , therefore, 1 = (-3)(-2)+b 1 = 6+b -6 -6 -5 =b
Write the equation of the new line: Y=-3x-5 Write the equation of the line: Perpendicular to y=3x-4 that passes through the point (3,2).
2=m(3)+b Slope is the neg. reciprocal so m=-1/3. 2=-(1/3)(3)+b 2=-1+b
3=b Equation: y=-1/3x+3 Parallel to the line 2x+y=6 thru (3,4). Perpendicular to the line -3x+ y=4 thru (6,4)