Problem 37 - Algebra 1: Concepts and Skills

Question

Graph the function. $$ g(x)=2 x-3 $$

Step-by-Step Solution

Answer

The graph of the line for the function \( g(x) = 2x - 3 \) crosses the y-axis at -3 and then rises with a slope of 2.

Step 1: Identify the Slope and Y-intercept

The equation given is \( g(x) = 2x - 3 \). In this case, the number 2 is the slope, and -3 is the y-intercept.

Step 2: Plot the Y-intercept

Begin drawing the graph by marking the y-intercept first. This is the point at which the line crosses the y-axis. In this case, the y-intercept is -3, which corresponds to point (0, -3). So, mark this point on your graph.

Step 3: Use the Slope to Identify Another Point

The slope tells you the vertical change (rise) for each unit of horizontal change (run). Since the slope is 2, this means that for each unit we move to the right on the x-axis, we move 2 units up on the y-axis. Starting from the y-intercept (0, -3), move 1 unit to the right and 2 units up. This leads you to point (1, -1). Mark this point on your graph.

Step 4: Draw the Line

With the two points (0, -3) and (1, -1) marked, draw a straight line through those points. This line represents the graph of the function \( g(x) = 2x - 3 \). Make sure the line extends beyond both points, with arrowheads at each end, indicating that the line extends indefinitely in both directions.