Explain the basic method(steps) for graphing a linear equation. Can you give an example of a linear equation and show me how to graph the equation?

5 x + 3 y = 15

first look at what happens when x = 0

3 y = 15
y = 5

Mark that point on your graph where x = 0 and y = 5
(0,5) Your y axis intercept
that is five units above the origin

Now what happens when y = 0?
5 x = 15
x = 3
So when y = 0 , x = 3
Mark that point on your graph
(3,0) Your x axis intercept
That is three units to the right of the origin

Now draw a straight line through those two points and you are finished.

You could have chosen any old values for x or y, but choosing zero makes it easy.
Your y axis intercept is when x = 0 and your x axis intercept is when y = 0

Sure! Graphing a linear equation involves a few basic steps. I'll explain the steps and then provide an example for further clarity.

1. Write the equation in slope-intercept form: The equation should be in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept (the value of y when x is zero).

2. Identify the slope and y-intercept: From the equation, you can determine the slope (m) and the y-intercept (b).

3. Plot the y-intercept: Locate the point (0, b) on the y-axis, where b is the y-intercept value you found in step 2.

4. Use the slope to find more points: Use the slope (m) to find additional points to plot on the graph. The slope represents the change in y divided by the change in x, which determines how steep the line is. Typically, the slope is expressed as a fraction or decimal.

- From the y-intercept, apply the slope: Starting from the y-intercept point, use the slope to calculate the change in y and x. Suppose the slope is 2/3, which means if you move three units to the right, you move two units up on the graph. Similarly, if the slope is -1/2, for every two units you move to the right, you move one unit down.

- Plot the additional points: Starting from the y-intercept, apply the slope to find points that are "connected" in a straight line. Plot these points on the graph. The more points you have, the more accurate your graph will be.

5. Draw the line: Once you have plotted multiple points, draw a straight line passing through those points. The line represents the graph of the linear equation.

Now, let's go through an example:

Example Linear Equation: y = 2x + 1

Step 1: The equation is already in slope-intercept form.

Step 2: The slope (m) is 2, and the y-intercept (b) is 1.

Step 3: Plot the y-intercept: The y-intercept is (0, 1).

Step 4: Use the slope to find more points: Since the slope is 2 (or 2/1), for every one unit you move to the right, you move two units up.

- Starting from the y-intercept (0, 1), move one unit to the right: This gives you the point (1, 3).

Step 5: Draw the line: Connect the points (0, 1) and (1, 3) with a straight line.

That's it! You have successfully graphed the linear equation y = 2x + 1. The line should pass through the plotted points, showing a positive slope.