# A line passes through (4 ,3 ) and (7 ,1 ). A second line passes through (1 ,1 ). What is one other point that the second line may pass through if it is parallel to the first line?

May 1, 2018

#### Answer:

The two lines have the same slope because they are parallel.

One point on the second line is $\left(\frac{3}{2} , 2\right)$.

#### Explanation:

In order to solve this question, we need to find the slope of the first line. The second will have the same slope, since they are parallel.

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$= \frac{1 - 3}{7 - 4} = - \frac{2}{3}$

If we write the equation of the second line as:

$y = m x + c$ we can substitute in the value of $m$:

$y = \frac{2}{3} x + c$

We can substitute in the point $\left(1 , 1\right)$ to find the value of $c$:

$1 = \frac{2}{3} \left(1\right) + c$

$c = \frac{1}{3}$

So $y = \frac{2}{3} x + \frac{1}{3}$

Any point that we can substitute into this equation that makes it true is a point on that line. Let's choose $y = 2$ and find the value of $x$ that makes the equation too:

$2 = \frac{2}{3} x + \frac{1}{3}$

$x = \frac{3}{2}$

One point on the second line, then, is $\left(\frac{3}{2} , 2\right)$.