What is slope and y intercept of 5x-10y=20?

2 Answers
May 15, 2018

The slope is 1/2, and the y intercept is -2

Explanation:

First, you get y by itself. That gives you -10y=-5x+20. Then you divide both sides by -10. That gives you y=1/2x-2. The slope is the number with the variable and the y intercept is the other number.


Mathematical explanation

  • 5x-10y=20
  • -10y=-5x+20
  • (-10y)/(-10)=(-5x)/(-10)+20/(-10)
  • y=(5/10)x-2
  • y=1/2x-2

Now recall the format y=\color(blue)(m)x+\color(red)(b), where m is the slope and b is the y-intercept.
From our equation, y=\color(blue)(1/2)x+(\color(red)(-2)), your slope is 1/2 and your y-intercept is -2.

May 15, 2018

color(white)("dddd")slope =color(white)(-)1/2

y-intercept = -2

Explanation:

Given: 5x-10y=20

Before we do anything else notice that all the value are exactly divisible by 5 so lets simplify.

Divide everything by 5

x-2y=4

To make the -2y positive multiply all of both sides by (-1)

-x+2y=-4

Add x to both sides

-x+2y=-4
ul(+x color(white)("dddd")=color(white)("dddd")+x )
0color(white)("d.")+2y=-4color(white)("d")+x

Divide both sides by 2

2/2y=-4/2+x/2

y=-2+1/2 x

Change the order to match convention

y=color(red)(1/2) xcolor(blue)(-2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The slope is the value in front of the x so the slope color(red)(=1/2)

The y-intercept (crosses the y-axis) is the constant of color(blue)(-2)