Given:
The graph given passes through two points (0, 2) and (-4, 8).
General Idea:
We can find the slope (m) of a line passing through two points say A and B using the below formula.
[tex] A(x_1,y_1) \; and \; B(x_2,y_2) \; the\; two\; points\\ \\ Slope\; (m)\; =\; \frac{y_2-y_1}{x_2-x_1} [/tex]
Applying the concept:
Slope of the line given using the two points (0, 2) and (-4, 8).
[tex] m=\frac{8-2}{-4-0}=\frac{6}{-4} =\frac{-3}{2} [/tex]
Out of the five options given , we need to check which options have slope as -6/4 or -3/2 by rewriting (if needed) the given to slope intercept form y =mx + b and compare the same.
Conclusion:
Rewriting the first option, the slope is -6/4 as shown below.
[tex] y=\frac{12-6x}{4}=\frac{12}{4} -\frac{6x}{4} =-\frac{6}{4}x+3 [/tex]
Rewriting the fourth option, the slope is -3/2 as show below.
[tex] -4y=6x+4\\ \\ \frac{-4y}{-4}=\frac{6x}{-4}+\frac{4}{-4} \\ \\ y=\frac{-3}{2}x-1 [/tex]
Rewriting the fifth option, the slope is -3/2 as shown below.
[tex] 2y+3x-5=0\\Subtract \; 3x\; and\; add\; 5\; on\; both\; sides\; of\; the\; equation\\ \\ 2y+3x-5-3x+5=0-3x+5\\ Combine\; like\; terms\\\\ 2y=-3x+5\\ [/tex]
Divide by 2 throughout the equation
[tex] \frac{2y}{2} =\frac{-3x}{2}+\frac{5}{2} \\ \\ y=\frac{-3}{2} x+\frac{5}{2} [/tex]
