Respuesta :
We are given slope-intercept form of the equation of a line as follows:
[tex]y\text{ = -}\frac{2}{3}\cdot x\text{ + 1}[/tex]We will use the general slope-intercept formulation and plug out the neccessary information to help us solve the problem:
[tex]y\text{ = }m\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ The slope of the equation = }\frac{-2}{3} \\ c\colon\text{ The y-intercept = +1} \end{gathered}[/tex]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:
[tex]m\text{ = }\frac{-2}{3}[/tex]To find the slope between two points we use the following formula:
[tex]m_{o\text{ }}=\frac{y_f-y_i}{x_f-x_i}[/tex]We will go ahead and calculate the slope for each of the given sets of points.
Option A: ( 3 , -2 ) & ( 6, 0 )
[tex]m_A\text{ = }\frac{0\text{ - (-2)}}{(6)\text{ - (3)}}\text{ = }\frac{2}{3}[/tex]
Option B: ( 2 , -2 ) & ( 6, 4 )
[tex]m_B\text{ = }\frac{4\text{ - (-2)}}{(6)-(2)}\text{ = }\frac{6}{4}\text{ = }\frac{3}{2}[/tex]Option C: ( 2, 0 ) & ( 2 , -1 )
[tex]m_C\text{ = }\frac{-1\text{ - 0}}{2\text{ - 2}}\text{ = }\infty[/tex]Option D: ( 5 , 0 ) & ( -1 , 4 )
[tex]m_D\text{ = }\frac{4\text{ - 0}}{-1\text{ - 5}}\text{ = -}\frac{4}{6}\text{ = -}\frac{2}{3}[/tex]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:
[tex]\textcolor{#FF7968}{m_D=m=-\frac{2}{3}}[/tex]Option D
