Guidance for Graphing Linear Equations by Plotting Points

Q1. Graph by plotting points: y = 3x + 2

Background

Topic: Linear Equations and Graphing

This question is testing your ability to graph a linear equation by plotting points. You will use the equation to find several pairs of (x, y) values and then plot them on a coordinate grid.

Key Terms and Formulas

• Linear Equation: An equation of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• Slope ($m$): The rate at which $y$ changes with respect to $x$.

• Y-intercept ($b$): The value of $y$ when $x = 0$.

Key formula:

$y = mx + b$

Step-by-Step Guidance

1. Identify the slope and y-intercept from the equation $y = 3x + 2$. Here, $m = 3$ and $b = 2$.

2. Choose several values for $x$ (for example, $x = -1$, $x = 0$, $x = 1$) and substitute them into the equation to find the corresponding $y$ values.

3. For each $x$ value, calculate $y$ using $y = 3x + 2$ and record the ordered pairs $(x, y)$.

4. Plot these points on the coordinate grid. Make sure to label each point clearly.

Try solving on your own before revealing the answer!

Final Answer: Graph of y = 3x + 2

The points you plot (such as $(-1, -1)$, $(0, 2)$, $(1, 5)$) will form a straight line. The slope is 3, so the line rises 3 units for every 1 unit it moves to the right. The y-intercept is at $(0, 2)$.

Once you plot at least two points and connect them, you will have the graph of the equation.