• Create and interpret equations of linear functions
• Identify and graph lines that are vertical or horizontal
• Graph straight lines by plotting points, using slope and y-intercept, and make changes like shifts to graphs
• Write equations for lines that run parallel or at a right angle to another line

Linear equations show up everywhere, even in hands-on work like carpentry. When skilled carpenters like Kiran need to make precise cuts, they often use measurements and equations to ensure accuracy. Think of the cutting surface as a coordinate plane, where each point represents a specific position measured in inches. By writing these cuts as equations, Kiran can easily repeat the same cut on multiple boards without having to remeasure each time.

Let’s start with a basic vertical cut. When carpenters make vertical cuts, the line runs straight up and down, parallel to the y-axis. Just like drawing a line on graph paper, we can describe this cut using a simple equation.

Now let’s look at horizontal cuts, which run parallel to the x-axis. These cuts are often used to trim boards to the right length or create level edges. Just like the vertical cut, we can represent these cuts with an equation.

Now that we’ve mastered straight cuts, let’s help Kiran with a more intricate design. Sometimes carpenters need to make a series of precise cuts to create decorative shapes or functional joints. Kiran wants to recreate a rhombus cut-out, which requires four carefully planned cuts that work together. Each cut will follow a specific line equation, and we need to find the exact endpoints to ensure the cuts meet perfectly.

After completing the rhombus design, Kiran has another project that requires precise cuts: creating a square opening for a post to fit through. This is a common task in carpentry, like making a hole for a fence post or a support beam. Getting these cuts exactly right is crucial – if the opening is too small the post won’t fit, and if it’s too large, the post won’t be secure.