# How to sketch a line after being given its equation?

• Jan 19th 2011, 11:34 AM
Jaaaaamie
How to sketch a line after being given its equation?
Hi,

This may seem really basic, and I hope for the sake of my learning that it is.

Basically I've been given an equation, y= 2x + 7.

From this I need to sketch a line and give the lines two points.

I've been researching for hours, can't seem to find a solution anywhere.

Any help?
• Jan 19th 2011, 11:41 AM
dwsmith
Quote:

Originally Posted by Jaaaaamie
Hi,

This may seem really basic, and I hope for the sake of my learning that it is.

Basically I've been given an equation, y= 2x + 7.

From this I need to sketch a line and give the lines two points.

I've been researching for hours, can't seem to find a solution anywhere.

Any help?

When x = 0, y = 7.

That is one point.

What is x when y = 0?
• Jan 19th 2011, 11:47 AM
Quacky
The easiest way is to just take 3 values of x, calculate their corresponding y values, and plot those points.

For example, if $\displaystyle x = -1$

$\displaystyle y = 2\times -1 + 7$
$\displaystyle =6$

$\displaystyle (-1, 6)$ is a point on the curve
You can calculate any points you wish, but don't take anything too large or too small.
Oh, you meant the intercepts. See the post above for those :P
• Jan 21st 2011, 05:30 AM
HallsofIvy
When Quacky says "take three values of x", that is a little bit of "overkill". Two points determine a line, but it is a good idea to use a third point to verify that it lies on the line given by the first two points.

You say "I need to sketch a line and give the lines two points." Perhaps your problem is that you about this backwards! You should first find the two points and then draw the line through them. For example, if the equation is y= 3x- 4, choose any two value of x you like, say x= 0 and x= 1 just because they are easy. If x= 1, y= 3(1)- 4= 3- 4= -1 so (1, -1) is one point on the line. If x= 0, y= 3(0)- 4= 0- 4= -4 so (0, -4) is another point. Mark those two points on a graph and draw the line through them.

As a check, and to make Quacky happy, choose a third value of x, say x= 2. y= 3(2)- 4= 6- 4= 2 so (2, 2) is a third point on the line. Check to see if that point is on the line. If it is, all is well!