Question

A line passes through (3, 7) and (6, 9). Which equation best represents the line? y = 3 over 2 x + 5 y = 2 over 3 x + 5 y = 3x + 2 y = 2 over 3 x + 2

Answer 1

Answer:
y = (2/3)x + 5

Explanation:
The general form of the linear line:
y = mx + c
where:
m is the slope
c is the y-intercept
First, we will compute the slope of the line:
slope (m) = (y2-y1) / (x2-x1)
m = (9-7) / (6-3)
m = 2/3
Then, we will compute the y-intercept:
The given points satisfy the equation of the line. So, we will use any of the given points (I will use point (3,7)) to substitute in the equation and solve for c as follows:
y = mx + c
y = (2/3)x + c
7 = (2/3)(3) + c
7 = 2 + c
c = 7-2
c = 5

Based on the above calculations, the equation of the line would be:
y = (2/3)x + 5

Hope this helps :)

Answer 2

Slope = (9 - 7)/(6-3) = 2/3

y = mx + b

b = y - mx
b = 7 -(2/3)(3)
b = 7 - 2
b = 5

equation
y = 2/3 x + 5

answer
y = 2 over 3 x + 5