Graph the line with the equation y = (3/4)x + 4.

Understand the Problem

The question is asking us to graph a line based on the given linear equation. The equation can be used to find points that lie on the line, which can then be plotted on a coordinate plane.

Answer

The line for the equation $y = \frac{3}{4}x + 4$ is graphed through points $(0, 4)$ and $(4, 7)$.

Steps to Solve

Identify the equation form

The equation given is in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, the slope $m = \frac{3}{4}$ and the y-intercept $b = 4$.

Plot the y-intercept

Start by plotting the y-intercept on the graph. The y-intercept occurs where $x = 0$. Thus, the point is $(0, 4)$.

Use the slope to find another point

The slope $m = \frac{3}{4}$ indicates that for every 4 units you move to the right (positive x-direction), you move up (positive y-direction) by 3 units.

From the point $(0, 4)$, move right 4 units to $(4, 4)$, then up 3 units to $(4, 7)$. Plot the point $(4, 7)$.

Draw the line

Now, draw a straight line through the points $(0, 4)$ and $(4, 7)$. Extend the line in both directions, adding arrows to indicate it continues infinitely.

The graph of the line representing the equation $y = \frac{3}{4}x + 4$ is correctly plotted with points at $(0, 4)$ and $(4, 7)$, extending infinitely in both directions.

More Information

In the equation $y = \frac{3}{4}x + 4$, the slope $\frac{3}{4}$ signifies that the line ascends as it moves to the right. The y-intercept at 4 means the line crosses the y-axis at that point. This is a common form used in linear equations to easily graph lines.

Tips

Ignoring the slope's direction: Remember that the slope indicates direction—positive slopes rise from left to right.
Incorrect points plotting: Ensure points are plotted accurately based on the slope and y-intercept; check coordinates carefully.

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