Question

Write an equation, in the slope intercept form of the line passing through the points $(2,3)$ and $(4,6)$

Answer 1

Since slope of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

We now find the slope of the line passing through the points $(2,3)$ and $(4,6)$ as shown below:

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

Therefore, the slope of the line is $\frac{3}{2}$.

Now use the slope and point $(2,3)$ to find the y-intercept.

$y=mx+b\Rightarrow 3=(\frac{3}{2}\times 2)+b\Rightarrow 3=3+b\Rightarrow b=3-3=0$

Write the equation in slope intercept form as:

$y=mx+b$

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

Hence, the equation of the line is $y=\frac{3}{2}x$..