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":

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting our values:

$m=\frac{3-1}{2-4}$

Solving the operations:

$\begin{gathered} m=\frac{2}{-2} \\ m=-1 \end{gathered}$

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:

$f(x)=-x+5$