what is the slope intercept form of
(8,3); m = 5
slope intercept form equation
(-10,-6); m = -5/8
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
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
To find the slope-intercept form of a linear equation, we need to use the equation: y = mx + b, where "m" represents the slope and "b" represents the y-intercept.
In the first scenario, we are given the point (8,3) and the slope "m" is 5.
Step 1: Start with the equation: y = mx + b
Step 2: Substitute the given values: 3 = 5(8) + b
Step 3: Simplify: 3 = 40 + b
Step 4: Isolate b by subtracting 40 from both sides: 3 - 40 = b
Step 5: Simplify: -37 = b
Therefore, the equation in slope-intercept form with a given slope and point is y = 5x - 37.
In the second scenario, we are given the point (-10,-6) and the slope "m" is -5/8.
Step 1: Start with the equation: y = mx + b
Step 2: Substitute the given values: -6 = (-5/8)(-10) + b
Step 3: Simplify: -6 = 50/8 + b
Step 4: Convert 50/8 to a decimal: -6 = 6.25 + b
Step 5: Isolate b by subtracting 6.25 from both sides: -6 - 6.25 = b
Step 6: Simplify: -12.25 = b
Therefore, the equation in slope-intercept form with a given slope and point is y = (-5/8)x - 12.25.