(0 2) (3 3) Slope Intercept Form

5 min read Jul 03, 2024

Slope Intercept Form: Understanding (0, 2) and (3, 3)

In algebra, the slope intercept form is a fundamental concept used to graph linear equations. It is a way to express a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. In this article, we will focus on understanding the slope intercept form using the points (0, 2) and (3, 3).

What is the Slope Intercept Form?

The slope intercept form is a linear equation written in the form of y = mx + b, where:

m is the slope, which represents the steepness of the line
b is the y-intercept, which is the point where the line crosses the y-axis

The slope intercept form is useful because it allows us to easily graph a linear equation and identify its key features, such as the x-intercept, y-intercept, and slope.

Finding the Slope Intercept Form using (0, 2)

Let's start by finding the slope intercept form using the point (0, 2). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

Since the point (0, 2) lies on the line, we can plug in x = 0 and y = 2 into the equation.

y = mx + b 2 = m(0) + b 2 = b

This tells us that the y-intercept (b) is 2. Now, we need to find the slope (m). Since we don't have enough information, let's assume the slope is m.

y = mx + 2

Finding the Slope Intercept Form using (3, 3)

Now, let's find the slope intercept form using the point (3, 3). We can use the same formula y = mx + b.

Plugging in x = 3 and y = 3 into the equation, we get:

y = mx + b 3 = m(3) + b 3 = 3m + b

Subtracting b from both sides gives:

3 - b = 3m

Dividing both sides by 3 gives:

1 - b/3 = m

Now we have two expressions for the slope intercept form: y = mx + 2 and y = (1 - b/3)x + b. We can set these two expressions equal to each other to find the value of b.

mx + 2 = (1 - b/3)x + b mx + 2 = x - bx/3 + b mx + 2 = x(1 - b/3) + b

Equating the coefficients of x, we get:

m = 1 - b/3

Substituting this value of m into one of the slope intercept forms, we get:

y = (1 - b/3)x + b y = x - bx/3 + b

Simplifying the equation, we get:

y = x - x/3 + 2 y = 2x/3 + 2

Conclusion

In this article, we used the points (0, 2) and (3, 3) to find the slope intercept form of a linear equation. We started by finding the y-intercept (b) using the point (0, 2) and then used the point (3, 3) to find the slope (m). By equating the two expressions, we found the slope intercept form to be y = 2x/3 + 2. This form allows us to easily graph the linear equation and identify its key features.