Determine the slope of the line that passes through the points 𝐴: two, negative five and 𝐵: four, five.
Slope is the ratio of the rise, which is the vertical change — the up and down change — to the run — the horizontal change moving left and right. So we are gonna find the slope that passes through these two points. Again, slope is the vertical change over the horizontal change. So if we imagine these two points on a graph, what would we have to look at for the vertical change? Well on a graph, the change going up and down is represented in the 𝑦-values.
So we need to know the change between negative five to five. And when we try to find the change between two points, that’s like the difference between two points; how far apart are they? Well, we need to find the difference between them. So we have negative five minus five. The horizontal change is what moves left and right. Those would be your 𝑥-values on a graph.
So for horizontal change, we need to look at the difference between the two and four; how far apart are they? We need to know difference between them. So right now, we have negative five minus five over two minus four. Negative five minus five is negative 10 and two minus four is negative two. Negative 10 divided by negative two is positive five because two negatives make a positive.
Now when it comes to slope, again it’s the vertical change over the horizontal change. So instead of five, we should have five over one. That means we are going to rise five spaces and run one space. So we go up five and right one and then up five and right one and then up five and right one. The reason I say this is because in linear functions no matter which two points you would choose on a line, the slope, which is the rate of change, is always gonna stay the same. So if you’re going between these two points, the slope is gonna be five over one, and this is going to be a line. Well anywhere on that line, it’s gonna keep the same slope — five over one. So the slope of the line that passes through the points 𝐴: two, negative five and 𝐵: four, five would be five over one.