📝 Practice Worksheets
🔑 Key Concepts
- Use both ordered pairs to calculate the slope with \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\).
- Substitute the slope and either known point into \(y=mx+b\).
- Solve the resulting equation to determine the y-intercept, \(b\).
- Substitute \(m\) and \(b\) into \(y=mx+b\) to write the final equation.
- Check that both original ordered pairs satisfy the completed equation.
💡 Main Idea
When two points are given, first use them to calculate the slope. Then substitute the slope and the \(x\)- and \(y\)-coordinates of either point into \(y=mx+b\). Solve for \(b\), and use the slope and y-intercept to write the equation in slope-intercept form.
🧠 Math Vocabulary
- Slope-intercept form: The form \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept.
- Slope: The rate of change between two points, calculated as change in \(y\) divided by change in \(x\).
- Y-intercept: The value of \(y\) where a line crosses the y-axis.
- Ordered pair: A point written as \((x,y)\).
- Substitution: Replacing a variable with a known value.
📚 What You Should Already Know
Before this lesson, students should understand ordered pairs, integer operations, substitution, solving one-step equations, and how to calculate slope from two points.
🚀 What Comes Next
Students can use the completed equation to graph the line, compare linear relationships, write equations from tables and graphs, and model real-world situations with slope and y-intercept.
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