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 Skip Navigation LinksMath Help > Geometry > Points and Lines > Graphing a Line

On 9/29/00 2:58:20 PM, Laura Dunaway wrote:

-x +2y=4

I'm terrible at Algebra! The teacher explained this so fast I couldn't see how to do it. We have to solve it and graph it! I don't know how to solve it!

To solve for y, you add the same number to both sides of the equation, or multiply both sides by the same (non-zero) number until y is by itself on one side of the equation.

I'll take it very slowly:

-x+2y=4
-x+x+2y=x+4
2y=x+4
(1/2)2y=(1/2)x+(1/2)4
y=(1/2)x+(1/2)4
y=(1/2)x+2

Now you have solved for y, and the equation is in a form called "slope intercept" form. That means you have y equals some number (the slope) times x plus some other number (the y-intercept). You may have seen the slope-intercept form described as

y=mx+b

In this form, m is the slope, and b is the y-intercept -- that's the place on the y axis where the graph of the line crosses the y axis.

In your equation, 

y=(1/2)x+2

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

You can begin plotting this by putting a dot on the y axis at the point where y=2. Then, since the slope is 1/2, you know that you go up 1 square for every 2 squares you move to the right. You can use this to plot one or two more points, then use a ruler to draw a line through the points.

If you write the slope as a fraction, the numerator is the number of squares you go up (if it's negative you go down), and the denominator is the number of squares you go to the right (you never go left, because you never write the denominator as a negative number).

A very high positive slope gives you a line that goes up a lot for every square you go to the right -- a steep slope that goes up and to the right (and down-left, too). A very small positive slope gives you a line that goes up just a little bit for every square you go to the right -- a gentle slope that goes up and to the right (and down-left, too).

A very "large" negative slope gives you a steeply sloped line that goes down and to the right (or up-left). A very "small" negative slope gives you a gentle slope that goes down and to the right (or up-left).

Zero slope is a horizontal line. The slope of a vertical line is undefined.


The webmaster and author of this Math Help site is Graeme McRae.