Welcome back to Math Mondays! Our blog prompt for today is to name some questions we could ask once we know the equation of a line. This ties into our Math curriculum for Chapter 7, which is what we are studying at the moment.
Lines can be translated to equations by using the formula y=mx+b. The formula uses variables as substitutes for vocabulary terms. "Y" and "X" are output and input, respectively. "M" stands for the slope of a line, which can be found by dividing a line's rise (change in y values) by its run (change in x values). "B" stands for the "y" intercept, which is found anywhere on the "y" axis and 0 on the x-axis.
I was a little confused by the blog assignment. What did he mean by "questions we could ask"? I've figured that a few sample questions you might ask after finding what a line's equation is would be "what are the rise and the run?" When you divide them together, you get "M". Our long-term substitute in math explained to us that the slope is usually represented as a ratio or a fraction. Fractions are parts of numbers designed to show division. We get this ratio by finding the change in "y" values from the y-intercept to our "y" coordinate and dividing it by the change in "x" values from the y-intercept to our "x" coordinate. This results in the slope. So, we could ask ourselves what the rise and run, respectively, are by counting the number of changes on our plotlines from our "y"-intercept to our coordinate.
This sounds really confusing, I know. But another question we could ask is "How can the slope be expressed differently?" If a slope is 0 - meaning that there are no changes from "x" to "y" coordinates, we say that the line is horizontal, or flat. There are a lot of terms for the slope. We also call the rise/run division problem the "rate of change" because it tells us how much change occurred when we moved in the coordinate plane. We can find out what the coordinates would be for any equation with the same slope but different variables by making a table and writing down what our input (x), rule (y=mx+b), and output (y) would be. This way it is easy to get a bigger and wider picture of what the slope of the function is.
Lines can be translated to equations by using the formula y=mx+b. The formula uses variables as substitutes for vocabulary terms. "Y" and "X" are output and input, respectively. "M" stands for the slope of a line, which can be found by dividing a line's rise (change in y values) by its run (change in x values). "B" stands for the "y" intercept, which is found anywhere on the "y" axis and 0 on the x-axis.
I was a little confused by the blog assignment. What did he mean by "questions we could ask"? I've figured that a few sample questions you might ask after finding what a line's equation is would be "what are the rise and the run?" When you divide them together, you get "M". Our long-term substitute in math explained to us that the slope is usually represented as a ratio or a fraction. Fractions are parts of numbers designed to show division. We get this ratio by finding the change in "y" values from the y-intercept to our "y" coordinate and dividing it by the change in "x" values from the y-intercept to our "x" coordinate. This results in the slope. So, we could ask ourselves what the rise and run, respectively, are by counting the number of changes on our plotlines from our "y"-intercept to our coordinate.
This sounds really confusing, I know. But another question we could ask is "How can the slope be expressed differently?" If a slope is 0 - meaning that there are no changes from "x" to "y" coordinates, we say that the line is horizontal, or flat. There are a lot of terms for the slope. We also call the rise/run division problem the "rate of change" because it tells us how much change occurred when we moved in the coordinate plane. We can find out what the coordinates would be for any equation with the same slope but different variables by making a table and writing down what our input (x), rule (y=mx+b), and output (y) would be. This way it is easy to get a bigger and wider picture of what the slope of the function is.
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