To find slope and y-intercept from the equation, we have to compare the given equation with slope intercept form
y = mx + b
Here m is slope and b is y-intercept
Find slope and y intercept of the line given below.
Problem 1 :
x + 4y = 8
Solution :
x + 4y = 8
The given equation is in standard form, to convert this equation to slope intercept form.
4y = - x + 8
Divide each side by 4.
y = -x/4 + 8/4
y = (-1/2) x + 2
The above equation is in the form y = mx + b
Then,
Slope (m) = -1/2
y-intercept (b) = 2
Problem 2 :
2x - 6y = -12
Solution :
2x - 6y = -12
-6y = -2x - 12
Divide each side by -6.
y = (-2/-6) x + (-12/-6)
y = (1/3) x + 2
The above equation is in the form y = mx + b
Then,
Slope (m) = 1/3
y-intercept (b) = 2
Problem 3 :
y = - 2
Solution :
y = 0x - 2
The above equation is in the form y = mx + b
Then,
Slope (m) = 0
y-intercept (b) = - 2
Problem 4 :
5x - y = 3
Solution :
5x - y = 3
-y = - 5x + 3
y = 5x - 3
The above equation is in the form y = mx + b
Then,
Slope (m) = 5
y-intercept (b) = - 3
Problem 5 :
-5x + 10y = 20
Solution :
-5x + 10y = 20
10y = 5x + 20
Divide each side by 10.
y = (5/10) x + (20/10)
y = (1/2) x + 2
The above equation is in the form y = mx + b
Then,
Slope (m) = 1/2
y-intercept (b) = 2
Problem 6 :
-x - y = 6
Solution :
-x - y = 6
-y = x + 6
y = - x - 6
The above equation is in the form y = mx + b
Then,
Slope (m) = - 1
y-intercept (b) = - 6
Problem 7 :
2.5x - 5y = - 15
Solution :
2.5x - 5y = - 15
-5y = -2.5x - 15
5y = 2.5x + 15
Divide each side by 5.
y = (2.5/5) x + (15/5)
y = 0.5 x + 3
The above equation is in the form y = mx + b
Then,
Slope (m) = 0.5
y-intercept (b) = 3
Problem 8 :
x = - 5/2
Solution :
x = - 5/2
Since x = - 5/2 is a vertical line, there is no y-intercept and the slope is undefined.
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