Use a graphing calculator to graph each linear equation on...

Use a graphing calculator to graph each linear equation on the same viewing window. Use a Trace or Intersect feature to find the point(s) of intersection.
$$\begin{aligned}
36 x-90 y &=-36 \\
-15.5 x-5 y &=-80.75
\end{aligned}$$

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Key Concepts

Linear Equations

Linear equations describe relationships between variables in a constant rate of change and are represented graphically by straight lines. Understanding how to form and manipulate these equations in formats like slope-intercept or standard form is foundational in algebra and analytic geometry.

Graphing Calculators

Graphing calculators are advanced tools that allow for the visualization of mathematical functions. They provide functionalities such as zoom, trace, and intersection features, which make it easier to explore the graphical representations of equations and analyze their behavior.

Systems of Equations

Systems of equations consist of two or more equations with the same variables. The graphical approach to solving these systems involves finding the point(s) where the graphs intersect, as these intersection points represent values that satisfy all equations simultaneously.

Trace and Intersect Features

The trace function on a graphing calculator lets users move along a graph and view coordinates at specific points, which is valuable for identifying key features of the graph. The intersect feature automatically calculates the coordinates of where two graphs cross, providing a clear solution to a system of equations.

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