Question

Write the equation of the line that passes through (3,3) and (1, -5). A) y = 4x - 9 B) y = -4x + 15C) y = xD) y = 4x + 12

Answer 1

Given these two points on the line:

`\begin{gathered} \mleft(3,3\mright) \\ \mleft(1,-5\mright) \end{gathered}`

You need to remember the Slope-Intercept Form of the equation of a line:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

The slope of a line can be found by using this formula:

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

Where these two points are on the line:

`\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}`

In this case, you can set up that:

`\begin{gathered} y_2=-5_{} \\ y_1=3 \\ x_2=1 \\ x_1=3 \end{gathered}`

Then, substituting values into the formula and evaluating, you get:

`m=(-5-3)/(1-3)=(-8)/(-2)=4`

In order to find the value of "b", you need to substitute the slope and the coordinates of one of the points, into this equation:

`y=mx+b`

Then, substituting values and solving for "b", you get:

`\begin{gathered} 3=(4)(3)+b \\ 3=12+b \\ 3-12=b \\ b=-9 \end{gathered}`

Therefore, knowing "m" and "b", you can write this equation of the line in Slope-Intercept Form:

`y=4x-9`

Hence, the answer is: Option A.