Answer:
The slope will be 2/5.
Step-by-step explanation:
[tex]y = 2/5x -1[/tex] is written in slope-intercept form.
This formula looks like:
[tex]y=mx+b[/tex]
where:
- M = Slope
- x = independent variable
- b = y-intercept
So:
- [tex]2/5[/tex] is our slope
- [tex]x[/tex] remains our independent variable
- [tex]-1[/tex] is our y-intercept.
1 ). For two lines to be parallel they must have the same slope.
2 ). For two line to be perpendicular they must have slopes that are opposite reciprocals.
- . Slope would become -5/2
As the question states, we must find the slope of a line parallel to the equation given. This means that the slope will remain 2/5.
Lets check our work!
Choose a random ordered pair. I will choose (5, 6).
Now, using point slope-form we can find out if what was said above is true!
This formula looks like:
[tex]y - y1 = m (x-x1)[/tex]
Let us substitute:
[tex]y - 6 = 2/5(x-5)[/tex]
Distribute:
[tex]y-6=2/5x-2[/tex]
Add 6 to both sides:
[tex]y= 2/5x+4[/tex]
Now using both equations I will plot them on a graph to see if they a parallel.
As you can see from the graph below, these lines are parallel. Where the equation you were given is in blue and the equation I made is in red.
Based on all of the evidence, the slope will be 2/5.
Hope this helped! :)
