Answer: The correct options are
(A) [tex]y=\dfrac{12-6x}{4},[/tex]
(D) [tex]-4y=6x+4,[/tex]
(E) [tex]2y+3x-5=0.[/tex]
Step-by-step explanation: We are given to select the equation that has the same slope as the given graph.
We can see that the graph is a straight line. And, (0, 2) and (-4, 8) are two points on the line graph.
So, the slope of the line in the graph will be
[tex]m=\dfrac{8-2}{-4-0}=\dfrac{6}{-4}=-\dfrac{3}{2}.[/tex]
We know that the slope-intercept form of a straight line is
[tex]y=mx+c,[/tex]
where m is the slope of the line.
Option (A):
The given equation of the line is
[tex]y=\dfrac{12-6x}{4}\\\\\\\Rightarrow y=-\dfrac{3}{2}x+3,[/tex]
so the slope of the line is [tex]-\dfrac{3}{2}.[/tex] Since the line has same slope as the one that is graphed, this option is correct.
Option (B):
The given equation of the line is
[tex]y=-3x+2,[/tex]
so the slope of the line is [tex]-3.[/tex] Since the line has different slope from the one that is graphed, this option is NOT correct.
Option (C):
The given equation of the line is
[tex]y=-\dfrac{2}{3}x,[/tex]
so the slope of the line is [tex]-\dfrac{2}{3}.[/tex] Since the line has different slope from the one that is graphed, this option is NOT correct.
Option (D):
The given equation of the line is
[tex]-4y=6x+4\\\\\\\Rightarrow y=-\dfrac{3}{2}x-1,[/tex]
so the slope of the line is [tex]-\dfrac{3}{2}.[/tex] Since the line has same slope as the one that is graphed, this option is correct.
Option (E):
The given equation of the line is
[tex]2y+3x-5=0\\\\\\\Rightarrow 2y=-3x+5\\\\\\\Rightarrow y=-\dfrac{3}{2}x+\dfrac{5}{2},[/tex]
so the slope of the line is [tex]-\dfrac{3}{2}.[/tex] Since the line has same slope as the one that is graphed, this option is correct.
Thus, the correct options are
(A) [tex]y=\dfrac{12-6x}{4},[/tex]
(D) [tex]-4y=6x+4,[/tex]
(E) [tex]2y+3x-5=0.[/tex]
