Question

How do you write an equation of a line with point $(3,-3)$ slope $3$?

Answer 1

Step 1 :Find the equation of a line with a given point and slope:

Equation of any line with a given coordinate point and slope is $(\mathrm{y}-{\mathrm{y}}_1)=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1)$.

Where, $({\mathrm{x}}_1,{\mathrm{y}}_1)$is the coordinate point and $\mathrm{m}$ is the slope of the line.

Step 2 : Form the equation of a line with point $(3,-3)$ slope $3$:

Here, $({\mathrm{x}}_1,{\mathrm{y}}_1)=(3,-3)$ and slope, $\mathrm{m}=3$.

$$\begin{gathered} (\mathrm{y}-{\mathrm{y}}_1)=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1) \\ \Rightarrow (\mathrm{y}-(-3\left)\right)=3(\mathrm{x}-3) \\ \Rightarrow (\mathrm{y}+3)=3x-9 \\ \Rightarrow \mathrm{y}=3x-12 \end{gathered}$$

Hence, the equation of the line with point $(3,-3)$, slope $3$ is $\mathrm{y}=3x-12$.