3 Ways To Convert X 4y 28 To Slope Intercept Form

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Converting linear equations from standard form to slope-intercept form can be a straightforward process, and it's a skill that's essential for solving a wide range of problems in algebra and beyond. In this article, we'll explore how to convert the equation 3x + 4y = 28 to slope-intercept form, and we'll do it in three different ways.

First, let's quickly review what slope-intercept form is. The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. In other words, it's the point where the line crosses the y-axis.

Method 1: Solving for y

One way to convert the equation 3x + 4y = 28 to slope-intercept form is to solve for y. This involves isolating y on one side of the equation. To do this, we'll start by subtracting 3x from both sides of the equation.

3x + 4y = 28 4y = -3x + 28

Next, we'll divide both sides of the equation by 4 to solve for y.

4y / 4 = (-3x + 28) / 4 y = -3/4x + 28/4 y = -3/4x + 7

And there we have it – the equation 3x + 4y = 28 in slope-intercept form.

Method 2: Using the Slope Formula

Another way to convert the equation 3x + 4y = 28 to slope-intercept form is to use the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. However, we don't have two points – we just have the equation. But we can still use the slope formula by rearranging the equation to get the slope.

First, let's rearrange the equation to get y by itself.

3x + 4y = 28 4y = -3x + 28 y = -3/4x + 7

Now, let's use the slope formula to find the slope. We can choose any two points on the line, but it's easiest to use the y-intercept (0, 7) and the point (4, 4).

m = (y2 - y1) / (x2 - x1) m = (4 - 7) / (4 - 0) m = -3/4

Now that we have the slope, we can use the point-slope form of a linear equation to write the equation in slope-intercept form.

y - y1 = m(x - x1) y - 7 = -3/4(x - 0) y = -3/4x + 7

And there we have it – the equation 3x + 4y = 28 in slope-intercept form.

Method 3: Graphing the Equation

A third way to convert the equation 3x + 4y = 28 to slope-intercept form is to graph the equation and find the y-intercept and slope from the graph. This method is a bit more visual, but it can be a helpful way to understand the relationship between the equation and the graph.

To graph the equation, we'll start by plotting two points on the line. We can choose any two points, but it's easiest to use the y-intercept (0, 7) and the point (4, 4).

Now, let's draw a line through the two points. The line should be straight, and it should cross the y-axis at the point (0, 7).

From the graph, we can see that the slope of the line is -3/4 and the y-intercept is 7. We can use this information to write the equation in slope-intercept form.

y = mx + b y = -3/4x + 7

And there we have it – the equation 3x + 4y = 28 in slope-intercept form.

Conclusion

Converting linear equations from standard form to slope-intercept form is an essential skill in algebra. In this article, we've explored three different methods for converting the equation 3x + 4y = 28 to slope-intercept form: solving for y, using the slope formula, and graphing the equation. Each method has its own strengths and weaknesses, and the best method will depend on the specific problem and the tools you have available.

We hope this article has been helpful in your journey to master linear equations. Do you have any questions or comments about converting equations to slope-intercept form? Share them in the comments below!