Slope and Y-Intercept from a Table of Values

Slope and Y-Intercept of a Line

Understanding Linear Equations

In College Algebra, a linear equation in two variables is commonly written in the form y = mx + b, where m is the slope and b is the y-intercept. The slope describes the rate of change of y with respect to x, and the y-intercept is the value of y when x = 0.

• Slope (m): The ratio of the change in y to the change in x between any two points on the line.

• Y-Intercept (b): The point where the line crosses the y-axis (i.e., when x = 0).

Finding the Slope from a Table of Values

Given a table of values, the slope can be calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

• Choose any two points from the table. For example, using (x₁, y₁) = (-2, -1.5) and (x₂, y₂) = (0, 0):

• $m = \frac{0 - (-1.5)}{0 - (-2)} = \frac{1.5}{2} = 0.75$

• Alternatively, using (0, 0) and (6, 4.5): $m = \frac{4.5 - 0}{6 - 0} = \frac{4.5}{6} = 0.75$

Identifying the Y-Intercept from a Table

The y-intercept is the value of y when x = 0. From the table:

• When x = 0, y = 0, so the y-intercept is b = 0.

Summary Table: Slope and Y-Intercept

x	y
-2	-1.5
0	0
6	4.5

Example: Writing the Equation of the Line

Using the values found:

• Slope: $m = 0.75$

• Y-Intercept: $b = 0$

• Equation: $y = 0.75x$

Applications

• Finding the slope and y-intercept is essential for graphing lines and understanding linear relationships in algebra.

• These concepts are foundational for solving systems of equations and modeling real-world scenarios.