Which Graph Matches The Equation Y 3 2 X 3

To determine which graph matches the equation y = 3/2 x + 3, we need to understand the structure of linear equations and how they translate into visual representations. This equation is in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 3/2 and the y-intercept is 3.

The slope of 3/2 means that for every 2 units you move horizontally (to the right), the line goes up by 3 units. The y-intercept of 3 tells us that the line crosses the y-axis at the point (0, 3). With this information, we can start sketching or identifying the correct graph.

First, plot the y-intercept at (0, 3) on the coordinate plane. From there, use the slope to find another point: move 2 units to the right and 3 units up to reach (2, 6). Connecting these two points with a straight line gives you the graph of the equation. The line should extend infinitely in both directions, maintaining the same slope throughout.

If you're looking at multiple graph options, the correct one will have these characteristics: it crosses the y-axis at 3, and for every 2 units moved to the right, it rises by 3 units. The line will be straight, and its steepness will reflect the slope of 3/2, which is a moderate incline—steeper than a slope of 1 but less steep than a slope of 2.

It's also helpful to test a few points to confirm the equation. For example, if x = 2, then y = (3/2)(2) + 3 = 3 + 3 = 6, so the point (2, 6) should be on the line. Similarly, if x = -2, then y = (3/2)(-2) + 3 = -3 + 3 = 0, so the point (-2, 0) should also lie on the line.

In summary, the graph that matches the equation y = 3/2 x + 3 is the one that passes through (0, 3) and (2, 6), with a consistent slope of 3/2. This visual and numerical approach ensures you can confidently identify or sketch the correct graph.

To determine which graph matches the equation y = 3/2 x + 3, we need to understand the structure of linear equations and how they translate into visual representations. This equation is in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 3/2 and the y-intercept is 3.

The slope of 3/2 means that for every 2 units you move horizontally (to the right), the line goes up by 3 units. The y-intercept of 3 tells us that the line crosses the y-axis at the point (0, 3). With this information, we can start sketching or identifying the correct graph.

First, plot the y-intercept at (0, 3) on the coordinate plane. From there, use the slope to find another point: move 2 units to the right and 3 units up to reach (2, 6). Connecting these two points with a straight line gives you the graph of the equation. The line should extend infinitely in both directions, maintaining the same slope throughout.

If you're looking at multiple graph options, the correct one will have these characteristics: it crosses the y-axis at 3, and for every 2 units moved to the right, it rises by 3 units. The line will be straight, and its steepness will reflect the slope of 3/2, which is a moderate incline—steeper than a slope of 1 but less steep than a slope of 2.

It's also helpful to test a few points to confirm the equation. For example, if x = 2, then y = (3/2)(2) + 3 = 3 + 3 = 6, so the point (2, 6) should be on the line. Similarly, if x = -2, then y = (3/2)(-2) + 3 = -3 + 3 = 0, so the point (-2, 0) should also lie on the line.

In summary, the graph that matches the equation y = 3/2 x + 3 is the one that passes through (0, 3) and (2, 6), with a consistent slope of 3/2. This visual and numerical approach ensures you can confidently identify or sketch the correct graph.