# Solving equations and finding intercepts

Find an equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form:

28) (8,0), m = -3

Find an equation of the line passing through the pair of points. Write the equation in slope intercept form

36) (4, 8) and (-3, 8)

Find an equation at the line satisfying the conditions given. Express your answer in standards form:

40) Parallel to 2y+x=7 and passing through (-5, -4)

42) Perpendicular to y=3x and passing through (-3, 2)

Determine whether the given ordered paid is a solution to the system of equations:

6) (-4, 2/3)

2x - 3(y - 5) = 5

6y = x + 8

Solve the system of equations by graphing. Check your solution.

10) 3x - y = 5

2x - 3y = -6

Find the solution of each system by the addition (elimination) method. Check your answers.

26) 5s + 9T = 6

4s + 3T = 15

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#### Solution Preview

28) Using the standard form of linear equation: y-0=-3(x-8)=3x-24, the equation is y=3x-24

36) Slope m=(8-8)/(-3-4)=0. Using the standard form of linear equation: y-8=0(x-4)=0, the equation is y=8

40) Transfer 2y+x=7 to standard form to get y=-x/2+7/2. Hence the slope m=-1/2. Since our target line is parallel to y=-x/2+7/2, the slope of our target line is m=-1/2. Since the target line passes through (-5,-4), using the standard form of linear equation: ...

#### Solution Summary

The solution gives detailed steps on solving a set of math questions including finding linear line for given condition and solve system of equations.

Graphs and Solving Linear Equations Word Problems (20 Problems)

Solve the following equations for the unknown.

1. 5x = 20

2. 7x - 3 = 18

Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph.

3. y = x + 3

4. y = -2x - 7

5. 2x + 3y = 9

6.

A consumer electronics company sells 6.7 million MP3 players per month at a price of $100 apiece; when the price is lowered to $80, the company sells 10.2 million players per month. How many MP3 players can the company expect to sell per month at a price of $75?

7.

The points (1,5), (4,5), and (1,0) represent three corners of a rectangle; find the coordinates of the fourth point.

8.

Seven inches are equivalent to 17.78 cm. Find the equation converting length in cm to length in inches. What is the length in inches of a 96.2 cm bar?

9.

Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).

10.

Sales tax in Pennsylvania is 6%. Create an equation for the total price (cost plus tax) of a purchase in PA in terms of its cost. How much would a person pay for a car whose cost is $32,000?

11. 6.2(x - 15.1) = 9.3(-x - 3.2)

12. x/3 - 7/8 = 2/5(x + 15/4)

Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph.

13. 7.1x - 3.9y = 1.4

14. 3x = -2

15.. 4.2x + 3.8y = 1.9

16.

A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?

17.

Find the area of a rectangle if three of its corners are (-0.1,-3.4), (-7.9,-3.4), and (-0.1,6.8).

18.

A temperature of 41 degrees F is equivalent to 278.2 degrees K, while a temperature of 86 degrees F is equivalent to 303.2 degrees K. Find the equation converting Kelvin temperature to Fahrenheit. What is the Fahrenheit temperature when it is 180 degrees K?

19.

Find an equation in slope-intercept form passing through the points (-6.2,18.1) and (-3.4,18.1).

20.

Tom buys $20,000 worth of stock, and sells it eight months later for $28,000. If he is required to pay 15% capital gains tax on his profits, how much tax will he pay?