I'll do the hard one, you do the easy one:
(-10,-6); m = -5/8
let y = (-5/8)x + b, sub in (-10,-6)
-6 = (-5/8)(-10) + b
-6 = 25/4 + b
b = -49/4
y = (-5/8)x - 49/4
what is the slope intercept form of
(8,3); m = 5
slope intercept form equation
(-10,-6); m = -5/8
2 answers
Slope intercept form equation of straight line:
y = m x + b
where:
m is the slope
b is the y-intercept
In tis case:
1.
( 8 , 3 ) mean x = 8 , y = 3
m = 5
y = 5 x + b
You know coordinates of one point ( 8 , 3 )
Replace x = 8 , y = 3 in equation:
y = 5 x + b
3 = 5 ∙ 8 + b
3 = 40 + b
Subtact 40 to both sides
3 - 40 = 40 + b - 40
- 37 = b
b = - 37
So:
y = 5 x + b
y = 5 x - 37
2.
1.
( -10 , - 6 ) mean x = - 10 , y = - 6
m = - 5 / 8
y = - ( 5 / 8 ) x + b
You know coordinates of one point ( -10 , - 6)
Replace x = -10 , y = - 6 in equation:
y = - ( 5 / 8 ) x + b
- 6 = - ( 5 / 8 ) ∙ ( - 10 ) + b
- 6 = 50 / 8 + b
- 6 = 2 ∙ 25 / 2 ∙ 4 + b
- 6 = 25 / 4 + b
Subtact 25 / 4 to both sides
- 6 - 25 / 4 = 25 / 4 + b - 25 / 4
- 24 / 4 - 25 / 4 = b
- 49 / 4 = b
b = - 49 / 4
So:
y = - ( 5 / 8 ) x + b
y = - ( 5 / 8 ) x - 49 / 4
y = m x + b
where:
m is the slope
b is the y-intercept
In tis case:
1.
( 8 , 3 ) mean x = 8 , y = 3
m = 5
y = 5 x + b
You know coordinates of one point ( 8 , 3 )
Replace x = 8 , y = 3 in equation:
y = 5 x + b
3 = 5 ∙ 8 + b
3 = 40 + b
Subtact 40 to both sides
3 - 40 = 40 + b - 40
- 37 = b
b = - 37
So:
y = 5 x + b
y = 5 x - 37
2.
1.
( -10 , - 6 ) mean x = - 10 , y = - 6
m = - 5 / 8
y = - ( 5 / 8 ) x + b
You know coordinates of one point ( -10 , - 6)
Replace x = -10 , y = - 6 in equation:
y = - ( 5 / 8 ) x + b
- 6 = - ( 5 / 8 ) ∙ ( - 10 ) + b
- 6 = 50 / 8 + b
- 6 = 2 ∙ 25 / 2 ∙ 4 + b
- 6 = 25 / 4 + b
Subtact 25 / 4 to both sides
- 6 - 25 / 4 = 25 / 4 + b - 25 / 4
- 24 / 4 - 25 / 4 = b
- 49 / 4 = b
b = - 49 / 4
So:
y = - ( 5 / 8 ) x + b
y = - ( 5 / 8 ) x - 49 / 4