How do you find a standard form equation for the line with the same x intercept as 9x - 2y + 18 = 0 and through the point (4,-5)?

Jun 10, 2016

$y = - \frac{5}{6} - 1 \frac{2}{3}$

Explanation:

First we have to find the $x$-intercept of the given line.
To find an $x$ intercept, make $y = 0$

$9 x - 2 \left(0\right) + 18 = 0 \text{ } \Rightarrow 9 x = - 18$

$x = - 2$ is the x-intercept. the coordinates are $\left(- 2 , 0\right)$

Now we have 2 points : $\left(- 2 , 0\right) \mathmr{and} \left(4 , - 5\right)$

Now you can use the method of finding the slope and substitute to find c,
However a quicker and easier method if you have 2 points is using the formula:

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

$\frac{y - \left(- 5\right)}{x - 4} = \frac{0 - \left(- 5\right)}{\left(- 2\right) - 4}$

$\frac{y + 5}{x - 4} = \frac{5}{- 6} = - \frac{5}{6} \text{ now cross multiply}$

$6 y + 30 = - 5 x + 20 \text{ simplify and make y = ...}$

$6 y = - 5 x - 10$

$y = - \frac{5}{6} - \frac{10}{6} \text{ } \Rightarrow y = - \frac{5}{6} - 1 \frac{2}{3}$