How do you graph a linear equation in slope-intercept form?

To graph a linear equation in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept, follow these steps:

1. Identify the slope, m.
2. Identify the y-intercept, b.
3. Plot the y-intercept on the graph, which is located at the point (0, b).
4. Use the slope, m, to find additional points on the graph by using the rise over run method. The rise over run method involves moving up or down from the y-intercept, depending on the sign of the slope, and then moving to the right or left based on the magnitude of the slope. For example, if the slope is 2/3, start at the y-intercept and move up 2 units and to the right 3 units to find a new point on the line.
5. Connect the points on the graph with a straight line.

It's important to note that the slope-intercept form is just one way to represent a linear equation. Other forms include point-slope form and standard form.

To graph a linear equation in slope-intercept form, you can follow these steps:

1. Find the y-intercept. This is the point where the line crosses the y-axis. To find it, set x to 0 and solve for y.
2. Find the slope. This is the ratio of the change in y to the change in x. To find it, calculate m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
3. Plot the y-intercept. This is the point (0, b).
4. Choose any other point on the line. To do this, start at the y-intercept and move up or down the y-axis by the slope, and then move to the right or left by 1 unit on the x-axis.
5. Connect the two points with a line.

For example, let's say we want to graph the equation y = 2x + 3.

1. The y-intercept is 3. This means the line crosses the y-axis at the point (0, 3).
2. The slope is 2. This means that for every 2 units we move up the y-axis, we must also move 1 unit to the right on the x-axis.
3. We can choose any other point on the line, such as (1, 5).
4. To plot (1, 5), we start at the y-intercept (0, 3) and move up 2 units to (0, 5). Then we move 1 unit to the right to (1, 5).
5. We connect the two points with a line. The graph of the equation y = 2x + 3 is shown below.

[asy] unitsize(1 cm);

draw((0,0)--(3,6));

label("$y$", (3,7), E); label("$x$", (7,0), N);

label("$3$", (0,3), S); label("$5$", (1,5), W); [/asy]