Question

(4,1) and (2,3) find the equation of the line passing through the given points. write in function notation.f(x)=

Answer 1

Step 1. We label the points to Find the slope of the line.

The points we have are (4,1) and (2,3), we label them as follows:

`\begin{gathered} x_1=4 \\ y_1=1 \\ x_2=2 \\ y_2=3 \end{gathered}`

Step 2. Use the slope formula to find the slope "m":

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

Substituting our values:

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

Solving the operations:

`\begin{gathered} m=(2)/(-2) \\ m=-1 \end{gathered}`

Step 3. Now that we have the slope, we use the point-slope equation to find the equation of the line.

The point-slope equation is:

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

Substituting the values of m, x1, and y1:

`y-1=-1(x-4)`

now we solve this equation for y by using the distributive property on the right side of the equation:

`y-1=-x+4`

Add 1 to both sides:

`\begin{gathered} y=-x+4+1 \\ y=-x+5 \end{gathered}`

Step 4. Change to function notation.

To do this, we change "y" for "f(x)":

`f(x)=-x+5`

Answer:

`f(x)=-x+5`