Question

How do you find the slope and y-intercept of the line $-7\mathrm{x}-9\mathrm{y}=27$ ?

Answer 1

Slope – intercept form:

The equation of the slope-intercept form is, $\mathrm{y}=\mathrm{mx}+\mathrm{b}$, where m is the slope, and b is the y-intercept.

Rewrite the equation in slope-intercept form:

The equation is $-7\mathrm{x}-9\mathrm{y}=27$.

Find the equation in the slope-intercept form :

$$\begin{gathered} \Rightarrow -9\mathrm{y}=7\mathrm{x}+27 \\ \Rightarrow -\mathrm{y}=\frac{7\mathrm{x}+27}{9} \\ \Rightarrow -\mathrm{y}=\frac{7\mathrm{x}}{9}+\frac{27}{9} \\ \Rightarrow -\mathrm{y}=\frac{7\mathrm{x}}{9}+3 \\ \Rightarrow \mathrm{y}=-\frac{7\mathrm{x}}{9}-3 \end{gathered}$$

Compare the equations and find the slope and y-intercept.

The obtained equation $\mathrm{y}=-\frac{7\mathrm{x}}{9}-3$ is of the form $\mathrm{y}=\mathrm{mx}+\mathrm{b}$.

Here, slope $\mathrm{m}=-\frac{7}{9}$and y-intercept $=-3$.

Hence the slope $m$ is $-\frac{7}{9}$and the $y$-intercept $b$ is $-3$ for the line $-7\mathrm{x}-9\mathrm{y}=27$ .