Linear equations

​ ​Here is a straight line drawn on a coordinate system. To get the exact information about both the line's position and slope, you can use a mathematical function, namely the equation of a straight line. This equation for this particular line is y=2x+1. The equation has the general form y=kx+m. This equation tells us two things.

First, when x increases y increases by twice as much. This is what the slope k says. Second, it tells us that when x is zero y is already at one. This is what plus one at the end says. M, therefore, tells us what the value of y is when x equals zero, or in other words, where the line crosses the y axis.

If the line was not drawn for us and we only had an equation like this, What would we do? Well, then we could draw the line ourselves. Make a table on a piece of paper. Let X be equal to 0 and write it in the table. You can now use the equation to calculate the corresponding value of y.

You'll get y=2. This you could actually see directly from the equation. It's the m value you calculated. Write it in the table. Then we give the value 0 to y and isolate x.

We get 2/3. Write this in the table as well. ​ ​Every row in the table represents the coordinates of the points in the line. One is where the line crosses the x axis, x intercept, and another one is where the line crosses the y axis, y intercept. Now it's time to draw the line. Start by drawing a horizontal and a vertical axis that together form a coordinate system.

Label the axis with x and y, and write numbers next to them. Take positions of two points from your table and mark them on the coordinate system. Use a ruler to draw a straight line through your point. Now we test it to see if it's right. Choose a third point on your line.

Take one that's easy to read. In this case where x equals one, add this point to your table as well. Put x and y of this point in to the equation and simplify. Now you don't have any unknowns in your equation. ​ ​So you can see if the equation is right? Yes, it's correct.

This means that the line you draw corresponds to the equation. The equation of a straight line gives you enough information to draw a straight line in a coordinate system. To do that draw a table and choose a value for x. Put the x value into the equation and solve it for y. Write down your y value in the table too.

You could do the opposite as well. Choose a y value and calculate x. Read the coordinates from the table, mark your points, and use a ruler to draw a straight line in the coordinate system. You need two points to draw a line, but feel free to calculate three just to be sure.