Question

Given the points (3, 2) and (6, 4), which of the following are true about the line passing through these points? The line has a slope of . The line represents a direct variation function. The line has a slope of . The point (-6, 9) is also on the line.

Answer 1

direct variation

Explanation:

Answer 2

The slope is 2/3 and the function is y=2/3x which is a direct variation function.

Explanation:

To find the slope of a line between two points, we use the equation

m = (y2-y1)/ (x2-x1)

where (x1,y1) and (x2,y2) are the two points

m= (4-2)/(6-3)

= 2/3

The slope of the line is 2/3

The equation of the line is

y-y1 = m(x-x1)

y-2 = 2/3(x-3)

Distribute

y-2 = 2/3x -2

Add 2 to each side

y-2+2 = 2/3x -2+2

y = 2/3x

This is a direct variation function

Let x = -6

y = 2/3(-6)

y = -4

(-6,-4)