# How do you name 3 lines that are not parallel to y= 5x -2?

Jan 13, 2017

see explanation.

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$y = 5 x - 2 \text{ is in this form and has a slope of 5}$

The following fact should be remembered.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{parallel lines have equal slopes}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

Thus writing an equation where m ≠ 5 , ensures that it is not parallel to the given equation. The value of b does not effect the slope.

The following are examples of 3 lines that are not parallel to the given line.

$m = 1 \to y = x$

$m = 3 \to y = 3 x - 1$

$m = - 2 \to y = - 2 x + 4$

The following sketch shows the graphs of.

$y = 5 x - 2 \text{ and } y = 3 x - 1$

graph{(y-5x+2)(y-3x+1)=0 [-20, 20, -10, 10]}