Question

Write an equation of the line in point slope from the passes through the given points (4,6) and (5,9)An equation of the line is_________

Answer 1

Since we have two points where the line passes through, first we need to find the slope between (4,6) and (5,9)

For that, we label the coordinates as:

`\begin{gathered} x_1=4 \\ y_1=6 \\ x_2=5 \\ y_2=9 \end{gathered}`

And we use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the values:

`\begin{gathered} m=(9-6)/(5-4) \\ m=(3)/(1) \\ m=3 \end{gathered}`

Now that we have the slope, we use the point slope equation:

`y=m(x-x_1)+y_1`

And we substitute the known values including the slope:

`\begin{gathered} y=3(x-4)+6 \\ \end{gathered}`

This is the equation in point slope form, if you need the slope intercept form (the simplified form) we do the following...

We use the distributive property to multiply 3 by x and 3 by -4:

`\begin{gathered} y=3x-12+6 \\ y=3x-6 \end{gathered}`

Answer: the equation of the line in point slople form is

`y=3(x-4)+6`

And the simplified form is

`y=3x-6`