How do you find a standard form equation for the line with (-3,6) and slope 7/8?

Apr 23, 2018

see a solution process below;

Explanation:

Recall, the standard form for the equation of a line is;

$y = m x + c$

Where;

$x \mathmr{and} y = \text{coordinates}$

$m = \text{slope}$

$c = \text{intercept}$

$y = m x + c - - - e q n \ast$

$x = - 3$

$y = 6$

$m = \frac{7}{8}$

Substituting the parameters into $e q n \ast$

$6 = \frac{7}{8} \left(- 3\right) + c$

$6 = - \frac{21}{8} + c$

Multiplying through by $8$

$8 \left(6\right) = 8 \left(- \frac{21}{8}\right) + 8 \left(c\right)$

$48 = \cancel{8} \left(- \frac{21}{\cancel{8}}\right) + 8 c$

$48 = - 21 + 8 c$

Collect like terms..

$48 + 21 = 8 c$

$69 = 8 c$

$c = \frac{69}{8}$

Substituting the value of $c$ into the main equation;

$y = m x + \frac{69}{8}$

Multiply through by $8$

$8 \left(y\right) = 8 m x + 8 \left(\frac{69}{8}\right)$

$8 y = 8 m x + \cancel{8} \left(\frac{69}{\cancel{8}}\right)$

$8 y = 8 m x + 69$

Recall; $m = \frac{7}{8}$

$8 y = 8 \left(\frac{7}{8}\right) x + 69$

$8 y = \cancel{8} \left(\frac{7}{\cancel{8}}\right) x + 69$

$8 y = 7 x + 69 \to \text{equation}$

Hope this helps!