Graphing and Writing Linear Equations
Lessons in this chapter
About Graphing and Writing Linear Equations
Graphing and Writing Linear Equations introduces slope as a core new idea, then uses it to graph and write linear equations in two different forms.
Graphs and Slopes of Linear Equations introduces slope: the ratio of vertical change to horizontal change between any two points on a line, and Graphing Proportional Relationships applies it to the special case of lines that pass through the origin, connecting directly back to 7th grade's Ratio and Proportion work.
Graphing Linear Equations in Slope-Intercept Form and Graphing Linear Equations in Standard Form cover the two most common ways a line’s equation is written, each with its own quick graphing method: slope and y-intercept for one, x- and y-intercepts for the other.
Writing Equations in Slope-Intercept Form and Writing Equations in Point-Slope Form reverse the process: given a slope and one point (or two points), write the equation of the line itself, the skill Systems of Linear Equations builds on next.
All six lessons are 8th grade math worksheets worked inside the page, so Graphs and Slopes of Linear Equations, Graphing Linear Equations in Slope-Intercept Form and Writing Equations in Point-Slope Form are sets of math problems with real graphs rather than a formula summary. Each answer is marked as it is entered, which is how a slope calculated as run over rise gets caught on the question itself. The chapter is free to try, with no login needed for your first 3.
Frequently asked questions
Graphs and Slopes of Linear Equations starts with slope as rise over run and what a positive, negative, zero or undefined slope looks like. Graphing Proportional Relationships covers the special case through the origin, then Graphing Linear Equations in Slope-Intercept Form and Graphing Linear Equations in Standard Form handle the two common forms. The last two lessons reverse the process: Writing Equations in Slope-Intercept Form from a graph or two points, and Writing Equations in Point-Slope Form. This sits in the Common Core domain Expressions and Equations (8.EE), and connects directly to Functions (8.F).
Slope is the ratio of vertical change to horizontal change between any two points on a line, often described as "rise over run": pick two points, subtract their y-values for the rise and their x-values for the run, then divide.
A proportional relationship is one where y is always the same constant multiplied by x, which always graphs as a straight line through the origin, Graphing Proportional Relationships has kids use that constant (the unit rate) directly as the line’s slope.
Slope-intercept form writes a line’s equation as y = mx + b, where m is the slope and b is the y-intercept: the point where the line crosses the y-axis, making both features readable directly from the equation.
Standard form writes a line’s equation as Ax + By = C, and it’s often faster for finding the x- and y-intercepts directly (by setting the other variable to 0), which is exactly how Graphing Linear Equations in Standard Form has kids graph it.
Use slope-intercept form: plug the known point’s x and y along with the slope into y = mx + b, solve for b, then write the final equation with both m and b known.