Answer:
A, C, F (see explanation)
Step-by-step explanation:
Notice that the x-values in the table include a pair that are symmetrical about x=0. That pair is -8 and 8. This means the y-intercept will be the average of the corresponding y-values, so will be (6+(-6))/2 = 0. When the y-intercept is zero, the table describes a proportion, and any y/x ratio will be the slope of the line. For example, using the middle table values, the slope is -3/4, a fraction that does not need to be reduced.
Given a slope of -3/4 and a y-intercept of 0, the slope-intercept form of the equation for the line can be written as ...
y = -3/4x
If we use the y-intercept as a point in the point-slope form, then that would give the equation ...
y -0 = -3/4(x -0)
y = -3/4x . . . . . . . the same equation as above
However, if we use one of the points in the table with the slope we found, we would get the equation ...
y -6 = -3/4(x +8) . . . . . using the first point in the table
Arguably, this is a different equation for the same line. If this equation is rearranged to slope-intercept form, it will be the same equation as above.
Whether your answer choice is A or B depends on how you interpret the meaning of "the same equation." (Here, I choose A, but I completely support B as a legitimate answer choice.)
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You can conclude ...
- A) Using either slope-intercept or point-slope forms will result in different equations.
- C) The slope is - 3/4.
- F) The y-intercept is 0.
