# If the slope is 7, and the given coordinates are (x , 8) and (4 , 1), how do you find x?

Jun 11, 2015

There's a formula for slope:

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

$\text{slope} = 7 = \frac{1 - 8}{4 - {x}_{1}} = \frac{1 - 8}{4 - x}$

$7 \left(4 - x\right) = - 7$

$28 - 7 x = - 7$

$35 = 7 x$

$x = 5$

And for the big picture:

$y = m x + b$

$1 = 7 \left(4\right) + b$
$b = - 27$

$y = 7 x - 27$ therefore has the points $\left(5 , 8\right)$ and $\left(4 , 1\right)$. You can find them here:

graph{7x -27 [-5.67, 14.33, -1.34, 8.66]}