Slope of a Line
Have you ever wondered how steep a hill was when riding a bike? Or hope that the road would become flat very soon! This idea of how steep something is or how flat it is, is why slope was created. We needed a way to communicate with each other about steepness and if we all used a different method to measure a steepness, well that would just be confusing. So, the idea of slope was created.
What is Slope?
Slope is the ratio that measures the steepness of a line. You will see slope represented with the variable, m in the United States. Why m? Great question and scholars are still debating and don’t have a great answer.
What is slope.pdfChange in Rise and Change in Run
Change in rise and change in run.pdfSo far, we have only looked at lines with positive slopes or lines that increase left to right. Let’s explore the different slopes a line can have:
Positive Slope
Positive Slope.pdfNegative Slope
Negative Slope.pdfSlope of 0
Slope of 0.pdfUndefined Slope
Undefined Slope.pdfHow do you calculate the slope of a line?
Many textbooks and websites will give you the slope formula to calculate the slope of a line. However, if you are like me, I don’t like to memorize when I don’t have to. So, let’s explore how to find the slope of line from a graph and a table and see if we can’t create our own slope formula that we don’t have to memorize but know how to derive or find every time we need to find the slope of a line. Our final challenge will be to use this idea to find the slope of a line given only two points.
Identify the slope of a line from a GRAPH:
Identify the slope of a line from a GRAPH.pdfCalculate slope of a line from a TABLE:
Calculate the slope of a line from a TABLE.pdfCalculate the slope of a line from TWO POINTS:
Calculate the slope of a line from TWO POINTS.pdfDeriving the Slope Formula
Deriving the Slope Formula.pdfWhy do we learn about slope?
why we learn about slope.pdfMath for Thought
Will a line with a positive slope and a line with a negative slope ALWAYS, SOMETIMES, or NEVER intersect?
Always!
What's Next: Check out the Linear Relationship Fundamental Linear Functions to see slope in action!
