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)
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