I agree with all your choices. First, you would convert all the equations to slope-intercept form.
Convert the initial equation 5x - 3y = 8 to get y = 5/3x + (-8/3)
We can't do anything with -5 = 3y = -8 because of the equal signs, therefore, option A is eliminated.
Option B in slope-intercept is y = 5x + -8, that is no where close to y = 5/3x + (-8/3), so B is eliminated.
Option C in slope-intercept form is y = 5/3x + (-8/3), the same as the initial equation, so choice C is correct.
Option D in slope-intercept form is y = 2.5/-1.5x + 4/-1.5, dividing the fraction results in y = -1.667x + -2.667, -1.667x is the equivalent of -5/3 and -2.667 is the equivalent of (-8/3). It does not matter if the slope is positive or negative, as long as they're the same. Choice D is correct.
Option E in slope-intercept form is y = -25/-15x + 8/-15, dividing -25/15x results in 1.667x, but 8/-15 is -0.534, -0.534 is not equal to -2.667. Choice E is eliminated.
Option F in slope-intercept form is y = -15/-9x + 24/-9, -15/-9 is 1.667 and 24/-9 is -2.667, this is equivalent to y = 5/3x + (-8/3). Choice F is correct.
I agree with all your answers! :)
