Question

Given the points (3, 2) and (6, 4), which of the following are true about the line passing through these points?

Answer 1

I don't know what 'which of the following' is referring to, but the line has a positive slope, goes through the origin, and has a slope of 2/3.

Answer 2

Given the points are A(3, 2) and B(6, 4).

If it is asking about the slope of the line AB, then we can use the slope formula as given by :-

`Slope, \;m = (y_(2)-y_(1))/(x_(2)-x_(1))`

where (x₁, y₁) = A(3, 2) and (x₂, y₂) = B(6, 4)

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

Hence, m = 2/3 would be slope of the line AB.

If it is asking about the y-intercept of the line AB, then we can use slope-intercept form as given by :-

y = mx + b

where m is the slope and b is the y-intercept.

we can plug the value of m = 2/3 and point A(3, 2) into the equation and solve for b.

`image`

Hence, b = 0 would be y-intercept of the line AB.

If it is asking for the equation of the line AB, then we can use slope-intercept form and put values of m = 2/3 and b = 0.

y = mx + b

`image`

Hence,
`y=(2)/(3) x \;\; or\;\; 3y=2x` would be equation of the line AB.