Question

Which line set of points are part of a line that is parallel to the line y = (-2/3)x + 11. (3,-2), (6,0)2. (2,-2), (6,4)3. (2,0), (2, -1)4. (5,0), (-1,4)

Answer 1

We are given slope-intercept form of the equation of a line as follows:

`y\text{ = -}(2)/(3)\cdot x\text{ + 1}`

We will use the general slope-intercept formulation and plug out the neccessary information to help us solve the problem:

`y\text{ = }m\cdot x\text{ + c}`

Where,

`\begin{gathered} m\colon\text{ The slope of the equation = }(-2)/(3) \\ c\colon\text{ The y-intercept = +1} \end{gathered}`

Now, we will use the above data of constants ( m and c ) and determine what parameters resembles an equation that is parallel to the given line.

We know for a fact that all parallel lines have the same gradient/slope/orientation in the cartesian coordinate system. Hence, we are looking for a line which has the same slope as the equation given in the question i.e:

`m\text{ = }(-2)/(3)`

To find the slope between two points we use the following formula:

`m_{o\text{ }}=(y_f-y_i)/(x_f-x_i)`

We will go ahead and calculate the slope for each of the given sets of points.

Option A: ( 3 , -2 ) & ( 6, 0 )

`m_A\text{ = }\frac{0\text{ - (-2)}}{(6)\text{ - (3)}}\text{ = }(2)/(3)`

Option B: ( 2 , -2 ) & ( 6, 4 )

`m_B\text{ = }\frac{4\text{ - (-2)}}{(6)-(2)}\text{ = }(6)/(4)\text{ = }(3)/(2)`

Option C: ( 2, 0 ) & ( 2 , -1 )

`m_C\text{ = }\frac{-1\text{ - 0}}{2\text{ - 2}}\text{ = }\infty`

Option D: ( 5 , 0 ) & ( -1 , 4 )

`m_D\text{ = }\frac{4\text{ - 0}}{-1\text{ - 5}}\text{ = -}(4)/(6)\text{ = -}(2)/(3)`

We will go ahead and compare the slopes determined for each pair of coordinate and see which option results in the same slope as the one " plugged out " from original equation.

Hence, The correct answer is:

`\textcolor{#FF7968}{m_D=m=-(2)/(3)}`

Option D