What is slope intercept form ?
The equation which is represented in the form y = mx + b is known as slope intercept form.
Here m is slope and b is the y-intercept.
To find equation of the line in slope intercept form, we have to follow the steps given below.
Step 1 :
Equation of line will be in the form
y - y_{1} = m(x - x_{1})
Here m is the slope and (x_{1}, y_{1}) is the point.
Step 2 :
Slope can be figured out with the formula
m = (y_{2} - y_{1})/(x_{2} - x_{1})
Step 3 :
After applying the point and slope in the respective places, we will get the equation in the form y = mx + b.
Find the equation of the line in slope intercept form with the given information.
Problem 1 :
m = -2 and goes through (-1, 4)
Solution :
Equation of the line passes through the point and slope
y - y_{1} = m(x - x_{1})
Here (x_{1}, y_{1}) is (-1, 4) and slope (m) = -2
(y - 4) = -2(x - (-1))
y - 4 = -2(x + 1)
y - 4 = -2x - 2
y = -2x - 2 + 4
y = -2x + 2
So, the required equation in slope intercept form is
y = -2x + 2
Problem 2 :
Goes through (1, 4) and (3, 10)
Solution :
Equation of the line passes through the point and slope
y - y_{1} = m(x - x_{1}) -----(1)
Here (x_{1}, y_{1}) is (1, 4) and (x_{2}, y_{2}) is (3, 10)
m = (y_{2} - y_{1})/(x_{2} - x_{1})
m = (10 - 4) / (3 - 1)
= 6/2
m = 3
Applying any one of the points given and slope in (1), we get
y - 1 = 3(x - 4)
y = 3x - 12 + 1
y = 3x - 11
Problem 3 :
Goes through (-4, -5) and (-1, -1)
Solution :
Equation of the line passes through the point and slope
y - y_{1} = m(x - x_{1}) -----(1)
Here (x_{1}, y_{1}) is (-4, -5) and (x_{2}, y_{2}) is (-1, -1)
m = (y_{2} - y_{1})/(x_{2} - x_{1})
m = (-1 + 5) / (-1 + 4)
m = 4/3
Applying any one of the points given and slope in (1), we get
y + 1 = (4/3) (x + 1)
3(y + 1) = 4(x + 1)
3y + 3 = 4x + 4
4x - 3y + 4 - 3 = 0
4x - 3y + 1 = 0
Problem 4 :
Goes through (3, 7) and (3, 9)
Solution :
y - y_{1} = m(x - x_{1}) -----(1)
Here (x_{1}, y_{1}) is (3, 7) and (x_{2}, y_{2}) is (3, 9)
m = (y_{2} - y_{1})/(x_{2} - x_{1})
m = (9 - 7) / (3 - 3)
m = 2/0
m = infinity
It must be a vertical line.
Applying any one of the points given and slope in (1), we get
y - 7 = (2/0) (x - 3)
0(y - 7) = 2(x - 3)
0 = 2(x - 3)
x = 3 is the required vertical line.
Problem 5 :
Solution :
From the graph given above, it is clear that y-intercept is at -2 and the point is (3, -3).
y = mx + b
y = -2x + b ---(1)
Applying the point (3, -3), we get
-3 = -2(3) + b
-3 = -6 + b
-3 + 6 = b
b = 3
Applying the value of b in (1), we get
y = -2x + 3
Problem 6 :
Solution :
Here (x_{1}, y_{1}) is (1, 1) and (x_{2}, y_{2}) is (5, 4)
m = (y_{2} - y_{1})/(x_{2} - x_{1})
m = (4 - 1) / (5 - 1)
= 3/4
Applying any one of the points given and slope in (1), we get
y - 1 = (3/4)(x - 1)
4(y - 1) = 3(x - 1)
4y - 4 = 3x - 3
3x - 4y - 3 + 4 = 0
3x - 4y + 1 = 0
Problem 7 :
Solution :
By observing the graph given above, the line passes through two points.
Here (x_{1}, y_{1}) is (-2, 2) and (x_{2}, y_{2}) is (2, 0)
m = (y_{2} - y_{1})/(x_{2} - x_{1})
m = (0 - 2) / (2 + 2)
= -2/4
= -1/2
Applying any one of the points given and slope in (1), we get
y - 0 = (-1/2)(x - 2)
2(y - 0) = -1(x - 2)
2y = -x + 2
Converting into slope intercept form, we get
y = (-1/2)x + 1
Problem 8 :
Solution :
By observing the graph given above, the line passes through two points.
Here (x_{1}, y_{1}) is (-3, -1) and y-intercept is -2
y + 1 = -2(x + 3)
y + 1 = -2x - 6
Converting into slope intercept form, we get
y = -2x - 6 - 1
y = -2x - 7
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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