Question

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

Answer 1

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 :-

$Slope, \;m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$m = \frac{4-2}{6-3} =\frac{2}{3}$

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.

$2=(\frac{2}{3} )(3) +b \\\\ 2 = 2 + b \\\\ b = 0$

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

$y=\frac{2}{3} x+0 \\\\ y=\frac{2}{3} x \;\; or\;\; 3y=2x$

Hence, $y=\frac{2}{3} x \;\; or\;\; 3y=2x$ would be equation of the line AB.

Answer 2

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.