Question

Explain how to solve a linear equation in one variable graphically.

Short answer

To solve a linear equation graphically, plot the y-intercept, then use the slope to find another point. Draw a line through these points and any point's x-coordinate on this line is a solution to the equation.

Step-by-step solution

Understand The Equation

A linear equation is usually in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. For simplicity, let's take a linear equation \(y = 2x + 3\) where '2' is the slope and '3' is the y-intercept.

Plot The Y-intercept

The y-intercept is the point on the graph where the line crosses the y-axis. So in this situation, the line will cross the y-axis at the point (0,3), marking this point on the graph.

Use The Slope To Find Other Points

The slope of the line is '2'. This means, for each step along the x-axis, the y-value goes up by 2. Plot a point at a convenient x-value. For example, at x = 1, y = 2*1 + 3 = 5. So, mark (1,5) on the graph.

Draw The Line

Now that we have two points, we can draw a line through these points. This line represents all solutions to the equation.

Use theGraph To Solve the Equation

The graph shows all the possible solutions for x and y that satisfy the equation \(y = 2x + 3\). So, just pick a point on the line, and use its x-coordinate as the solution to the equation.