Question

Choose the correct letter no need to show any work

Answer 1

Given that the line passes through these points:

`\mleft(4,3\mright),\mleft(7,9\mright)`

You can find the slope of the line using this formula:

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

Where these two points are on the line:

`(x_1,y_1),(x_2,y_2)_{}`

In this case, you can set up that:

`\begin{gathered} y_2=9 \\ y_1=3 \\ x_2=7 \\ x_1=4 \end{gathered}`

Substituting values into the formula and evaluating, you get:

`m=(9-3)/(7-4)=(6)/(3)=2`

By definition, the Slope-Intercept Form of the equation of a line is:

`y=mx+b`

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

In order to find the value of "b", you can substitute the slope and the coordinate of one of the points on the line into the equation, and then solve for "b":

`\begin{gathered} 3=(2)(4)+b \\ 3-8=b \\ b=-5 \end{gathered}`

Therefore, you get that the equation of this line in Slope-Intercept Form is:

`y=2x-5`

Since you must write the equation in Standard Form:

`Ax+By=C`

Where A, B and C are numbers.

You need to subtract the x-term from both sides of the equation:

`\begin{gathered} (-2x)+y=2x-5-(2x) \\ \\ -2x+y=-5 \end{gathered}`

Hence, the answer is: Option D.