Question

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Answer 1

We have two points and we have to find the line that includes them both.

The points are: (3,4) and (7,2).

We can start with a point-slope equation of the line, using the point (3,4):

$\begin{gathered} y-y_1=m(x-x_1) \\ y-4=m(x-3) \end{gathered}$

We now have to find the value of the slope m. We can find it by replacing the 2nd point, (7,2), in the equation:

$\begin{gathered} y-4=m(x-3) \\ 2-4=m(7-3) \\ -2=m(4) \\ m=-\frac{2}{4} \\ m=-\frac{1}{2} \end{gathered}$

Now, we can write the equation of the line as:

$\begin{gathered} y-4=-\frac{1}{2}(x-3) \\ y=-\frac{1}{2}x+\frac{1}{2}\cdot3+4 \\ y=-\frac{1}{2}x+\frac{3}{2}+4 \\ y=-\frac{1}{2}x+\frac{3+4\cdot2}{2} \\ y=-\frac{1}{2}x+\frac{11}{2} \end{gathered}$

We can graph this line and verify if it includes both points:

Both points are included.

Equation of the line: y = -(1/2)*x + 11/2