Answer
$$x-5y=-23$$
Work Step by Step
Recall the formula for slope:
$$slope(m)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, x2 - x1\ne0$$
Given the points $(2, 5)$ and $(-3, 4)$, we can find the slope:
$$slope(m)=\frac{4-5}{-3-2}$$ $$slope(m)=\frac{-1}{-5}$$ $$slope(m)=\frac{1}{5}$$
Recall the slope-intercept form: $y=mx+b$
Use either of the points and the computed value of the slope to find the intercept, $b$.
$Point\:1 (2,5)$
$m=\frac{1}{5}$
$$y=mx+b$$ $$5=(\frac{1}{5})(2)+b$$ $$5=\frac{2}{5}+b$$
Subtract $\frac{2}{5}$ from both sides:
$$5-\frac{2}{5}=\frac{2}{5}-\frac{2}{5}+b$$ $$\frac{25}{5}-\frac{2}{5}=b$$ $$\frac{23}{5}=b$$
Thus, we have the equation $y=\frac{1}{5}x+\frac{23}{5}$.
Rewriting this in the form $Ax + By = C$:
$$-\frac{23}{5}=\frac{1}{5}x-y$$ $$\frac{1}{5}x-y=-\frac{23}{5}$$
Multiply the whole equation by $5$:
$$[\frac{1}{5}x-y=-\frac{23}{5}]\cdot5$$ $$x-5y=-23$$