Linear Equations Objectives Find slope of a line

Linear Equations Objectives: -Find slope of a line - write 3 different forms of linear equations Ms. Olifer

SLOPE E P LO S RISE RUN

Slope Formula Given points (X 1, Y 1) and (X 2, Y 2) Is the same as ?

Example ( 4 , 0 ) and ( 7 , 6 ) (X 1, Y 1) (X 2, Y 2)

Example ( -6 , 5 ) and ( 2 , 4 ) (X 1, Y 1) (X 2, Y 2)

Example ( 5 , 2 ) and ( -3 , 2 ) (X 1, Y 1) (X 2, Y 2)

Example ( 2 , 7 ) and ( 2 , -3 ) (X 1, Y 1) (X 2, Y 2)

Recap of slope

Linear Forms of Linear Equations Standard Form (AX + BY = C) 1) A and B cannot be fractions. 2) A cannot be negative y = 3 x – 5 y – 3 x = – 5 – 3 x + y = – 5 3 x – y = 5 FINDING INTERCEPTS To find y-intercept, set x = 0 Y-intercept (0, -5) To find x-intercept, set y = 0 X-intercept (5/3, 0)

Linear Forms of Linear Equations Slope Intercept Form (y = mx + b) 1) Y is isolated on one side. 2) Y is positive x – 2 y = 6 – 2 y = – x + 6 y = ½ x + 6/-2 y= ½x– 3 FINDING INTERCEPTS To find y-intercept, set x = 0 Y-intercept (0, -3) To find x-intercept, set y = 0 X-intercept (6, 0)

Find a line || to 2 x + 4 y = -8 and passes thru (8, 3) • First find slope • 2 x + 4 y = -8 • 4 y = -2 x – 8 • y=-½x– 2 • Slope • • • Slo p ei nt e rc ep t Use y = mx + b y = - 1/2 x + b Plug in point 3 = - ½ (8) + b FINAL 3 = -4 + b EQUATION 7=b y = mx + b y=-½x+7

Find a line Perpendicular to 3 x – 2 y = 10 and passes thru (-6, 2) First find slope 3 x – 2 y = 10 - 2 y = -3 x + 10 y = 3/2 x – 5 c • • • Slope • • • Slo p ei nt e rc ep t Use y = mx + b y = -2/3 x + b Plug in point 2 = -2/3 (-6) + b 2 = 4+ b FINAL EQUATION -2 = b y = mx + b y = -2/3 x - 2

Find a line That has slope = 2 and passes thru (-4, 7) • • • Slo p ei nt e rc ep t Use y = mx + b y = 2 x + b Plug in point 7 = 2 (-4) + b 7 = -8 + b FINAL EQUATION 15 = b y = mx + b y = 2 x + 15

Find a line That has x-intercept = (5, 0) and y-intercept (0, -3) • First find slope • m = 3/5 • Use y = mx + b • y = 3/5 x + b • Plug in point either one ! • 0 = 3/5 (5) + b • 0= 3+b • -3 = b Slo p ei nt e rc ep t FINAL EQUATION y = mx + b y = 3/5 x - 3

First Let’s Review. . . Graphing Linear Equations

Graph x = 3

Graph y = -3

Graph Y = -3/4 x + 2 Y = mx + b m = slope b = y-intercept m = -3 / 4 b=2 1) 2) Plot the y-intercept first Starting from the y-intercept, go up if + or down if – Then go right. 3) Plot point and draw your line.