1. Find the slope-intercept form equation of the straight line with slope 2 and y-intercept 5.
2. Find the slope and y-intercept of the straight line whose equation is 4x - 2y + 1 = 0.
3. A straight line has the slope 5. If the line cuts y-axis at -2, find the equation of the line in slope-intercept form.
4. Find the slope-intercept form equation of the straight line passing through the point (-5, -4) with slope 3.
5. Find the equation of the line in slope-intercept form.
6. Find the slope-intercept form equation of the straight line passing through the point (1, 2) and parallel to the line whose equation is x + 2y + 3 = 0.
7. Find the slope-intercept form equation of the straight line passing through the point (-2, 3) and perpendicular to the line whose equation is x - 2y - 6 = 0.
8. A manufacturer produces 80 units of a particular product at a cost of $ 220000 and 125 units at a cost of $ 287500. Assuming the cost curve to be linear, find the cost of 95 units.
1. Answer :
Given : Slope = 2 and y-intercept form = 5.
Equation of the straight line in slope-intercept form :
y = mx + b
Substitute m = 2 and b = 5.
y = 2x + 5
2. Answer :
Write the given equation 4x - 2y + 1 = 0 in slope-intercept form.
4x - 2y + 1 = 0
4x + 1 = 2y
Divide each side by 2.
(4x + 1)/2 = y
2x + 1/2 = y
or
y = 2x + 1/2
The above form is slope intercept form.
If we compare y = 2x + 1/2 and y = mx + b, we get
m = 2 and b = 1/2
3. Answer :
Because the line cuts y-axis at -2, clearly y-intercept is -2.
Now, we know that slope m = 5 and y-intercept b = -2.
Equation of a straight line in slope-intercept form is
y = mx + b
Substitute m = 5 and b = -2.
y = 5x - 2
4. Answer :
Equation of the straight line in slope-intercept form.
y = mx + b
Substitute m = 2/3.
y = 3x + b -----(1)
Given : The line is passing through the point (-5, -4).
Then,
-4 = 3(-5) + b
-4 = -15 + b
Add 15 to each side.
11 = b
Substitute b = 11 in (1).
y = 3x + 11
5. Answer :
The above line is a falling line. So, its slope will be a negative value.
Measure the rise and run.
For the above line, rise = 4 and run = 3
slope = rise/run
= -4/3
The line in the diagram above intersects y-axis at -1.
So, y-intercept is -1.
Equation of the line in slope intercept form :
y = mx + b
Substitute -4/3 for m and -1 for b.
y = -4x/3 - 1
6. Answer :
Write the equation of the line x + 2y + 3 = 0 in slope intercept form.
x + 2y + 3 = 0
2y = -x - 3
y = (-1/2)x - 3/2
Because the required line is parallel to the given line, the slopes are equal.
Then, slope of the required line is -1/2.
So, equation of the required line in slope-intercept form is
y = (-1/2)x + b ----(1)
Given : The line is passing through the point (1, 2).
(1)----> 2 = (-1/2)(1) + b
2 = -1/2 + b
Add 1/2 to each side.
2 + 1/2 = b
5/2 = b
Substitute b = 5/2 in (1).
(1)----> y = (-1/2)x + 5/2
7. Answer :
Write the equation of the line x - 2y - 6 = 0 in slope intercept form.
x - 2y - 6 = 0
-2y = -x + 6
2y = x - 6
y = (1/2)x - 3
So, slope of the given line is 1/2.
Because the required line is perpendicular to the given line, product of the slopes is equal to -1.
Let 'm' be the slope of the required line.
m x (1/2) = -1
m/2 = -1
m = -2
So, equation of the required line in slope-intercept form is
y = -2x + b -----(1)
Given : The line is passing through the point (-2, 3).
(1)----> 3 = -2(-2) + b
3 = 4 + b
Subtract 4 from each side.
-1 = b
Substitute b = -1 in (1).
(1)----> y = -2x - 1
8. Answer :
Step 1 :
Since the cost curve is linear, the function which best fits the given information will be a linear-cost function.
y = Ax + B
y ----> Total cost
x ----> Number of units
Step 2 :
Target :
We have to find the value of 'y' for x = 95.
Step 3 :
From the question, we have
x = 80, y = 220000
x = 75, y = 287500
Step 4 :
When we substitute the above values of 'x' and 'y' in
y = Ax + B,
we get
220000 = 80A + B
287500 = 75A + B
Step 5 :
When we solve the above two linear equations for A and B, we get
A = 1500, B = 100000
Step 6 :
From A = 1500 and B = 100000, the linear-cost function for the given information is
y = 1500x + 100000
Step 7 :
To estimate the value of 'y' for x = 95, we have to substitute 95 for x in
y = 1500x + 100000
= 1500 x 95 + 100000
= 142500 + 100000
= 242500
So, the cost of 95 units is $242500.
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