Answer:
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'
- When two lines are parallel, they have the same slope.
Since 'n' and 'q' are parallel,
then the slope of q = ⁵/₃
- When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
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]
