Question

Hello I am really struggling with this type of math this problem is so bad

Answer 1

Answer:

The correct option is B

The equation of the line is:

`y=(9)/(2)x-24`

Step-by-step explanation:

Given the points: (4, -6) and (6, 3)

The equation of a line is given as:

`y=mx+b`

Where m is the slope and b the y-intercept

The slope is obtained as follows:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ =(3-(-6))/(6-4)=(3+6)/(2)=(9)/(2) \end{gathered}`

With m = 9/2, we have the line as:

`y=(9)/(2)x+b`

Now, we find the y-intercept, using either of the given points.

Using (6, 3), x = 6, y = 3

`\begin{gathered} 3=(9)/(2)(6)+b \\ \\ 3=27+b \\ b=3-27=-24 \end{gathered}`

Therefore, the equation is:

`y=(9)/(2)x-24`