1.) Write an equation of a line given
•The points (1,6) & (3,-4) •1.) Find the Slope
•m = (-4 -6)/(3-1) •m = -10/2 = -5
Write an equation of a line given
•The points (1,6) & (3,-4) •2.) Plug in one of the points
(y - y1) = m(x - x1)
•
(y - 6) = -5(x - 1) • y - 6 = -5x + 5
Write an equation of a line given
•
y - 6 = -5x + 5 •y - 6 + 6 = -5x + 5 + 6 • y = -5x + 11
Today’s Objective
•To be able to Re-Write and equation in Standard Form. •Ax + By = C…… where •A,B & C are real numbers
Equations of Lines
•Vertical line x=# •Horizontal line y = # •Slope, y-intercept y=mx+b •Point, Slope y-y1=m(x-x1) •Standard Form Ax+By = C
1.) Writing an equation in Standard Form Ax + By = C
•
y = 2/5x - 3
st 1
•The step is to multiply both sides by 5.
• y = 2/5x - 3 • (5)y = (2/5x - 3)5 • 5y = 2x - 15 • 5y -2x = 2x -2x - 15 •-2x + 5y = -15
1.) Writing an equation in Standard Form Ax + By = C
Writing an equation in Standard Form Ax + By = C
•
y = 1/2x + 4
st 1
•The step is to multiply both sides by 2.
You Try This One
• y = 1/2x + 4 • (2)y = (1/2x + 4)2 • 2y = x + 8 • 2y -x = x -x + 8 • -x + 2y = 8
Writing an equation in Standard Form Ax + By = C
2.) Writing an equation in Standard Form Ax + By = C
•
y = 0.55x + 1.35
st 1
•The step is to multiply both sides by 100.
2.) Writing an equation in Standard Form Ax + By = C
• •
•(100) y = (0.55x + 1.35)100
y = 0.55x + 1.35
100y = 55x + 135
•100y -55x = 55x -55x + 135
•-55x + 100y = 135
•Since all 3 TERMS are divisible by 5, we can simplify by dividing both sides by 5. •(-55x + 100y)/5 = 135/5 •-11x + 20y = 27
-55x + 100y = 135
Writing an equation in Standard Form Ax + By = C
•
y = 0.7x + 1.3
st 1
•The step is to multiply both sides by 10.
You Try This One
2.) Writing an equation in Standard Form Ax + By = C
•
•
y = 0.7x + 1.3
(10) y = (0.7x + 1.3)10
•
•
10y = 7x + 13
10y -7x = 7x -7x + 13
•-7x + 10y = 13
•1.) (3,4) m = 6 • y - y1 = m(x - x1) • y - 4 = 6(x - 3) • y - 4 = 6x - 18 •y - 4 + 4 = 6x - 18 + 4 • y = 6x - 14
Write the equation
Write the equation
•2.) y-intercept = 3, slope=2
•y = 2x + 3
Write the equation
•3.) (6,-2) & (-4, 4) •m = (4 - -2)/(-4 - 6) •m = 6/-10 = - 3/5 •y - y1 = m(x - x1) •y - 4 = -3/5(x - -4)
Write the equation
• y - 4 = -3/5(x - -4) • y - 4 = -3/5x - 12/5 •y - 4 + 4= -3/5x - 12/5 + 4 • y = -3/5x + 8/5