Question

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

Answer 1

see explanation.

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

`y=5x-2" is in this form and has a slope of 5"`

The following fact should be remembered.

`color(red)(bar(ul(|color(white)(2/2)color(black)("parallel lines have equal slopes")color(white)(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=1toy=x`

`m=3toy=3x-1`

`m=-2toy=-2x+4`

The following sketch shows the graphs of.

`y=5x-2" and " y=3x-1`

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