3 Easy Ways To Convert 3x 2y 16 To Slope Intercept Form

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Converting linear equations from standard form to slope-intercept form is a fundamental skill in algebra. The equation 3x + 2y = 16 is a typical example of a standard form equation that needs to be converted. In this article, we will explore three easy ways to convert 3x + 2y = 16 to slope-intercept form.

Understanding the Slope-Intercept Form

Before we dive into the methods, let's quickly review the slope-intercept form of a linear equation. The slope-intercept form is y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of the line, while the y-intercept is the point where the line crosses the y-axis.

Method 1: Solving for y

The first method is to solve the equation 3x + 2y = 16 for y. To do this, we need to isolate y on one side of the equation.

3x + 2y = 16

Subtract 3x from both sides:

2y = -3x + 16

Divide both sides by 2:

y = (-3/2)x + 8

In this form, we can see that the slope (m) is -3/2, and the y-intercept (b) is 8.

Method 2: Using the Slope Formula

The second method is to use the slope formula to find the slope of the line. The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

First, we need to find two points on the line. We can do this by substituting values of x into the equation 3x + 2y = 16. Let's say we choose x = 0 and x = 1.

When x = 0, we get:

3(0) + 2y = 16

2y = 16

y = 8

So, the point (0, 8) is on the line.

When x = 1, we get:

3(1) + 2y = 16

3 + 2y = 16

2y = 13

y = 13/2

So, the point (1, 13/2) is on the line.

Now, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (13/2 - 8) / (1 - 0)

m = (13/2 - 16/2) / 1

m = -3/2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. Let's use the point (0, 8).

y - 8 = (-3/2)(x - 0)

y - 8 = (-3/2)x

y = (-3/2)x + 8

This is the same equation we found in Method 1.

Method 3: Graphing the Line

The third method is to graph the line and then find the equation of the line. We can graph the line by plotting two points and drawing a line through them. Let's use the points (0, 8) and (1, 13/2).

Once we have graphed the line, we can see that the slope is -3/2, and the y-intercept is 8.

Using the slope-intercept form, we can write the equation of the line as:

y = (-3/2)x + 8

This is the same equation we found in Methods 1 and 2.

In conclusion, converting 3x + 2y = 16 to slope-intercept form is a straightforward process that can be done in three easy ways: solving for y, using the slope formula, or graphing the line. Each method yields the same equation: y = (-3/2)x + 8.

We hope this article has helped you understand the different methods for converting linear equations to slope-intercept form. If you have any questions or need further clarification, please leave a comment below.