# Equations

1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients.

2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form.

3.Determine the equation of the line through the points (4, 0) and (-3, -5). Write the equation in slope-intercept form.

4.After 2 minutes on a treadmill , Jenny has a heart rate of 82. After 3 minutes, she has a heart rate of 86. Assuming that Jenny's heart rate h is a linear function of time t in minutes, write h as a linear function of t. What heart rate could be expected for Jenny after 10 minutes on the treadmill? Solve by writing equations and solving them.

5.The cost C of natural gas is a linear function of the number n of cubic feet of gas used. The cost of 1000 cubic feet of gas is $39, and the cost of 3000 cubic feet of gas is $99. Express C as a linear function of n. What is the cost of 2400 cubic feet of gas? Solve by writing equations and solving them.

6.Determine whether the following are functions or not. Explain your answer.

a. {(1, 3), (1, -3), (2, 12)}

b. {(1, 3), (2, 3), (3, 3)}

c. {(1, 3), (2, 1), (3, 1)}

#### Solution Preview

1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients.

Equation in the slope intercept form is y=mx + c

We have one point (-2,0)

Thus 0 = m (-2) + c

or c= 2m

Thus the equation is y = m x + 2 m

where m is the slope

Answer: y =m x + 2 m

2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form.

slope of the line 3x + 5y = 15 is -3/5

A line parallel to this line will have this slope

Thus the equation of the line is y =( -3/5) x + c

This line also passes through (0,9)

Thus 9 = - (3/5) (0) + c

or c= 9

Thus the equation of the line is y =( -3/5) x + 9

Answer: y =( -3/5) x + 9

3.Determine the equation of the line through the points (4, 0) and (-3, -5). Write the equation in slope-intercept form.

y = mx + c

This line passes through (4,0) and ...

#### Solution Summary

Equations of straight lines are determined. For 2 problems, equations are formulated and solved.