# slope, intercept, equality, system of equations problems

1. Find the values of x and y that solve the following system of equation

-5x - 7y = 12

9x - 5y = -4

2. The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers?

3. Find an equation of the line that is parallel to the line y = 2x - 5 and that passes through the point (8,2)

4. 14x + 3y = -13

y= -11x + 27

does this equation belong to

(3,-6) or (-4,-9) or (2,5)

5. Filipe spent $24 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?

6. Evaluate the expression

9 + -24 - 1

7. The surface area S of a right prism is given by

S = 2B + Ph

Where B is the area of the base, P is the perimeter of the base, h is the height of the prism. Solve for h

8. The perimeter of a rectangular field is 338 yards, if the width of the field is 78 yards, what is its length in yards?

9. graph each line

y = -x + 2

x -2y = -2

9. graph the line with slope -1 passing through the point (2,-4)

10. Find the slope of the line (8,6)and (4,-3)

11. Find the x intercept and y intercept of the line given by the equation

7x + 2y = 12

12. Write an equation of the line with points at (0,0) and (3,6)

13. a line passes through the point (4,5) and has a slope of 3. Write an equation for the line.

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#### Solution Summary

This is a multi-question problem that involves a) graphing a straight line given two points, b) graphing two straight lines to find the solution, c) finding the x- and y-intercepts given the equation, d) writing the equation of a linear given the slope and a point, e) solving problems that have two variables, f) finding the equation of a line given two points.

Find the slope of any line perpendicular to the line through points

16. Find the slope of any line perpendicular to the line through points (0, 5) and (-3, -4).

20. on page 626

27. Geometry. Floor plans for a building have the four corners of a room located at the points (2, 3), (11, 6), (_3, 18), and (8, 21). Determine whether the side through the points (2, 3) and (11, 6) is parallel to the side through the points (_3, 18) and (8, 21).

Only answer 28, 27 is only used as a reference.

28. Geometry. For the floor plans given in exercise 27, determine whether the side through the points (2, 3) and (11, 6) is perpendicular to the side through the points (2, 3) and (_3, 18).

Write the equation of the line passing through each of the given points with the indicated

slope. Give your results in slope-intercept form, where possible.

6. (0, 5), m =

Write the equation of the line passing through each of the given pairs of points. Write your

result in slope-intercept form, where possible

20. (-1, 3) and (4, -2)

24. (2, -3) and (2, 4)

Write the equation of the line L satisfying the given geometric conditions.

36. L has y-intercept (0, -3) and is parallel to the line with equation y=

40. L has y-intercept (0, 2) and is perpendicular to the line with equation 2x - 3y = 6.

52. Business and finance. In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.

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