1.Write an equation of the line containing the given points and parallel to the given line (3,8); x+5y=3
2. Write an equation of the line containing the given points and parallel to the given line (-3,6); 5x=9y+2
3. Write an equation of the line containing the given points and perpendicular to the given line (4,5); 9x+y=7
4. Write an equation of the line containing the given points and perpendicular to the given line (5,-2); 9x+2y=7
5. Media Services charges $30 for a phone and $20/month for its economy plan. Find a model that determines the total cost, C(t), of operating a Media Services phone for t months. C(t)=?
Check 7-13-11, 11:40pm post for solution.
1. To get the equation of a line parallel to the given line, we need to find the slope of the given line first because parallel lines have the same slope. The given line is x + 5y = 3. To find the slope, we rearrange the equation to solve for y: 5y = -x + 3 -> y = (-1/5)x + 3/5. Since the coefficient of x is -1/5, the slope of the given line is -1/5.
Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope. Choose the point (3,8) from the given points. Plug in the values: y - 8 = (-1/5)(x - 3) -> y - 8 = (-1/5)x + 3/5. Simplify the equation to get the final equation: y = (-1/5)x + 43/5.
2. Similar to question 1, we need to find the slope of the given line 5x = 9y + 2. Rearrange the equation to solve for y: 9y = 5x - 2 -> y = (5/9)x - 2/9. The slope of the given line is 5/9.
Using the point-slope form, choose the point (-3,6) from the given points. Plug in the values: y - 6 = (5/9)(x + 3) -> y - 6 = (5/9)x + 15/9. Simplify the equation to get the final equation: y = (5/9)x + 33/9.
3. To get the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line. The given line is 9x + y = 7. Rearrange the equation to solve for y: y = -9x + 7. The slope of the given line is -9.
The negative reciprocal of -9 is 1/9, so the slope of the perpendicular line is 1/9. Choose the point (4,5) from the given points. Use the point-slope form: y - 5 = (1/9)(x - 4) -> y - 5 = (1/9)x - 4/9. Simplify the equation to get the final equation: y = (1/9)x + 41/9.
4. Following the same steps as question 3, we need to find the negative reciprocal of the slope of the given line 9x + 2y = 7. Rearrange the equation to solve for y: 2y = -9x + 7 -> y = (-9/2)x + 7/2. The slope of the given line is -9/2. The negative reciprocal of -9/2 is 2/9.
Choose the point (5,-2) from the given points. Use the point-slope form: y - (-2) = (2/9)(x - 5) -> y + 2 = (2/9)x - 10/9. Simplify the equation to get the final equation: y = (2/9)x - 28/9.
5. To find the total cost, C(t), of operating a Media Services phone for t months, we can use the equation:
C(t) = cost of the phone + (monthly cost x t)
The cost of the phone is $30, and the monthly cost is $20. Plugging in the values, the equation becomes:
C(t) = 30 + (20t)
Therefore, the model that determines the total cost of operating a Media Services phone for t months is C(t) = 30 + (20t).