Question

Sketch a graph of the equation. $$ 2 x-y-3=0 $$

Short answer

The graph of the equation \(y = 2x - 3\) is a straight line with a slope of 2 and crossing the y-axis at -3.

Step-by-step solution

Transform the equation

Start by adding \(y\) to both sides of the equation to isolate it on one side: \(2x - 3 = y\). This is the same as \(y = 2x - 3\).

Identify slope and y-intercept

In this slope-intercept form, the slope \(m\) is 2 and the y-intercept \(b\) is -3.

Plot y-intercept on graph

The y-intercept is the point at which the line crosses the y-axis. In this case, the y-intercept is -3, so the first dot should be placed at (0,-3) on the graph.

Use the slope to plot the second point on graph

From the y-intercept, use the slope to find the second point on the graph. In this case, the slope is 2, or \(2/1\), which means move 2 units up (positive direction on y-axis) and 1 unit to the right (positive direction on x-axis) from the y-intercept. This gives second point (1,-1).

Draw the line

Connect the two points on the graph to create the line that represents the equation.