Question

Which statement about the points (5, 7) and (10, 12) is true? CLEAR CHECK There is not enough information to determine if the points show direct variation. They show direct variation because y = x + 2 and 10 – 5 = 12 – 7. The line they are on does not show direct variation. They show direct variation because the line they are on has a positive slope.

Answer 1

Explanation:

direct variation means that

y = kx

that means it is a line with y-intercept = 0.

in other words, when x = 0, then y = 0 too.

for 2 given points the first part is automatically true. 2 points always define a line.

so, what we need to find out is, if (0, 0) is also on the line.

if not, it is not a direct variation.

the 2 points imply the equation

y = x + 2

as the y value is always larger than the x value by 2.

this has a y-intercept larger than 0 (2).

and so, (0, 0) is NOT on the line, and it is NOT a direct variation.

so, the 3rd answer option is correct.