Now, let's say if we're given an equation in point-slope form. How can we graph this equation on a coordinate plane? What would you do in order to graph it? Now, the first thing you should do is identify the slope.
and the point, the x-y ordered pair. So here's the original equation. So we can see that the slope is equal to 2. So m is 2. And then we can see that x1 is positive 1, not negative 1, but positive 1. And y1 is positive 3. So we have the point 1, 3. x is 1 and y is positive 3. is 3. So what you want to do is plot the point first.
1, 3 is over here and the slope is equal to 2. That means as you travel 1 unit to the right, you need to go up 2 units. So the next point is going to be at 2, 5. So if you go 1 to the left, you need to go down 2 units. Now granted, this line is not going to be perfectly straight, but...
You get the picture. And then just connect them with a straight line. Let's try another example.
So let's say if we have this equation, y plus 3 is equal to 3 over 2 times x plus 4. So, identify the slope and the point. We can see that the slope is equal to 3 over 2. Now, what's x1 and what's y1? x1 is negative 4, y1 is negative 3. Basically, you just got to change the sign of these numbers. If you see a plus 4, make it a negative 4. If you see a positive 3, make it a negative 3. If you see a negative 3, make it a positive 3. So just reverse the signs, and you're going to get the point, which is negative 4 comma negative 3. So now we can go ahead and plot it. The first point is at negative 4, negative 3. And the slope is 3 over 2. 3 is the rise, 2 is the run.
So we're going to travel 2 units to the right, and we're going to go up 3 units. So the next point that we're going to get is negative 2, 0. X is negative 2, Y is 0. So now let's use the slope again. Let's travel 2 units to the right, and let's go up 3 units. So this will take us to the point 0, 3. which is a y-intercept of 3. And now let's connect these points.
So now you know how to graph a linear equation in point-slope form. So all you need to do is find the x and y values of the point, the first point they need to plot, and then use the slope to get the next point. All you need is two points.
If you have two points, you can draw a straight line. If you want a third point, that's fine too, but you just need two points at minimum to graph a straight line.