What are the equations of lines m and q?

The equation of line m is:

  Equation of 'm'

   (y - 6) = - ³/₅ (x - 2)     [point-slope form]

           y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

    Equation of 'q'

     (y - 6) = ⁵/₃ (x - 2)         [point-slope form]

            y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

Step-by-step explanation:

To find the equation for both 'm' and 'q' requires a bit of work. Because neither  'm' nor 'q' has two points to find the slopes of the line, we have to get creative.

Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line.  Luckily for us, line 'n' is parallel with 'q' and perpendicular with m.

Finding the slope of 'n'

The slope of the 'n'    =  (y₂ - y₁) ÷ (x₂ - x₁)      

                                    =  (4 - (- 1)) ÷ (4 - 1)  

                                    =  5 ÷ 3

                                    =  ⁵/₃

Determine the slope of 'q' and 'm'

            Since 'n' and 'q' are parallel,

                           then the slope of q = ⁵/₃

             Since 'n' and 'm' are perpendicular

                           then the slope of m = - ³/₅

Write the equation for 'q' and 'm'

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines

For both 'q' and 'm' let (x₁, y₁) be (2, 6)

    Equation of 'm'

   (y - 6) = - ³/₅ (x - 2)     [point-slope form]

           y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

    Equation of 'q'

     (y - 6) = ⁵/₃ (x - 2)         [point-slope form]

            y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above