# How do you determine the the missing coordinate of A(_, 0), B(5, 10) if the slope is 2?

Jun 13, 2015

${x}_{1} = 0$

#### Explanation:

Consider that the slope $m$ is:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$m = 2 = \frac{10 - 0}{5 - {x}_{1}}$
so that rearranging:
${x}_{1} = 0$

Jun 13, 2015

Let $\left({x}_{1} , {y}_{1}\right) = A = \left({x}_{1} , 0\right)$ and $\left({x}_{2} , {y}_{2}\right) = B = \left(5 , 10\right)$

Then slope $2 = m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{10 - 0}{5 - {x}_{1}} = \frac{10}{5 - {x}_{1}}$

Hence ${x}_{1} = 0$

#### Explanation:

Slope $m$ is given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

where the line passes through points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$

In our example, we are given $m$, ${y}_{1}$, ${x}_{2}$ and ${y}_{2}$ and we are trying to find the value of ${x}_{1}$.

Putting our known values into the equation for slope, we get:

$2 = \frac{10 - 0}{5 - {x}_{1}} = \frac{10}{5 - {x}_{1}}$

Multiply both ends by $\left(5 - {x}_{1}\right)$ to get:

$10 = 2 \left(5 - {x}_{1}\right) = 10 - 2 {x}_{1}$

Subtract $10$ from both sides to get:

$- 2 {x}_{1} = 0$

Divide both sides by $- 2$ to get:

${x}_{1} = 0$