And hopefully you're seeing now that if I were to keep going, and I encourage you though if you want pause the video and try x equals three or x equals negative one and keep going. When x is equal to two y is equal to one. Now let's see, if x isĮqual to two what is y? Two times two is four, minus three is one. So we move positive one in the x direction and negative one, or down If x is equal to one, what is y equal to? Well two times one is two, In the vertical direction, in the y direction. And on our coordinate plane here that's- we're gonna move zero in the x direction, zero in the horizontal direction and we're gonna go down three So, if x is equal to zero y is gonna be two times zero minus three which is negative three. So, I'm just gonna pick some x values and make it easy to calculate Let's see, let's plot some of the xy pairs that satisfy this equationĪnd then feel good that it does indeed generate a line. That's why it's called a linear equation. Them on the coordinate plane, you would actually get a line. The set of all of the xy pairs that satisfy this equation and if you were to graph Now why do we call it a linear equation? Well if you were to take So, for example the equation y is equal to two x minus three, this is a linear equation. And just to start ourselves out, let's look at some examples

Introduce you to in this video is the idea of a Linear Equation. We conclude that the graph of any linear equation in x and/or y is always a straight line.

The slope is the constant m, so the graph of y=mx+b is a straight line. The distinctness of x_1 and x_2 avoids division by 0 when we find the slope. For any two distinct points on the graph, the x-coordinates, say x_1 and x_2, are also distinct (since the same value of x would give the same value of y because y is given explicitly in terms of x). This is clearly a vertical line through (a, 0).įor the form y=mx+b, if we can show that the slope is constant, then the graph must be a straight line.

(Yes, this already includes the form where y is a constant, because this would be the result of taking m to be 0 in the equation y=mx+b).įor the form x=a, the graph is the set of all points with constant x-coordinate a. In x and/or y, any linear equation is equivalent to one of two forms: x=a or y=mx+b where a, m, and b are constants.

Khan academy algebra linear