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# Equations

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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.

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

##### Solution Summary

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

##### 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 ...

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