Question

What is the equation of the line (in slope-intercept form) through the points (2,3) and (4,9)

Answer 1

The equation of the line in slope-intercept from would be y=3x-3.
3x is the slope also known as the rise over run.
-3 is the y-intercept, where the line cross the y-axis on the graph.

Answer 2

1) We have to find the slope of the line passes through these points.
Given two points, (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)

We have two points: (2,3) and (4,9), therefore the slope of the line passes through these points will be:
m=(9-3)/(4-2)=6/2=3

2)line in slope intercept form:
y=mx+b
m=slope
b=y-intercept

We know the slope of the line, but we have to find "b"
We can chooso either of these points (2,3) or (4,9), the result will be the same.
For example: we choose the point (2,3)
Then ; when x=2 ; the value of "y" will be 3 (y=3).
y=mx+b
3=3(2)+b
6+b=3
b=3-6
b=-3

We know the slope (m=3) and y-intercept (b=-3)
therefore:
y=mx+b
y=3x-3


Answer: y=3x-3