Objective- To write a linear equation given a point and a slope.
Write a linear equation in standard form given: slope = 3 m=3 y = mx + b y = 3x + -2 -3x -3x
Not in standard form!
y-intercept = -2 b = -2
-3x + y = -2
or
Ax + By = C Where A, B and C are integers.
3x - y = 2
Write a linear equation in standard form given: slope = 2 y-intercept = 4 3
y = mx + b y= 2 x+4 - 2x
3 3 - 2 x 3
3 3 - 2 x + y = 4 3
- 2 x + y = 4
Not in standard form! Ax + By = C Where A, B and C are integers. No fractional coefficients!
or
- 2x + 3y = 12
2x - 3y = -12
Write a linear equation in standard form given: slope = -1 point = (2,4) 5 (x,y)
5 4 = -2 + b 5 + 2 + 2 5 5
5
y = mx + b y = -1 x + b 5 4 = -1 (2) + b
y = -1 x + 22
5 5 + 1x 5
+
1x 5
5 1 x + y = 22 5 5 x + 5y = 22
4 2 = b = 22
5
Write a linear equation in standard form given: slope = -3 point = (1,-2) 7 (x,y)
7 3 -2 = -7 + b + 3 + 3 7 7
y = mx + b y = -3 x + b 7 -2 = -3 (1) + b
y = -3 x + -11
7 7 + 3x 7 7
+
3x 7 7
7 3 x + y = -11
7 -14 + 3 = b = -11 7 7 7
-2 + 3 = b
3x + 7y = -11
Write a linear equation in standard form given: slope = 3 x-intercept = 4 5 (x,y) 5 0 = 3 (4) + b 5 0 = 12 + b 5 - 12 - 12 5 5
y = mx + b y= 3 x+b
(4,0)
y = 3 x + -12
5 5 3 x 5 5
-
-
3x 5 5
5 -3 x + y = -12
0 +-12 = b = -12
5
-3x + 5y = -12
or
5
3x - 5y = 12
A hardware store sells extension ladders. A 16 ft. ladder costs $50 and the price increases $7.50 for each additional foot. If x = ladder length and y = price, write an equation for y in terms of x.
Slope Change in price = $7.50/ ft. m = 7.50 y = mx + b y = 7.50x + b 50 = 7.5(16) + b 50 = 120 + b -120 -120 -70 = b
Point 16 ft. cost $50 (x, y) = (16, 50)
y = 7.5x - 70