3 Vocabulary Terms - Define/Illustrate
1. Slope-intercept Form 2. Standard Form 3. Point-Slope Form
1. Slope-Intercept Form: This is a common linear equation format, represented as y = mx + b. In this form, "m" represents the slope of the line and "b" represents the y-intercept, which is the point where the line crosses the y-axis.
Illustration:
Consider the equation y = 2x + 3. Here, the slope is 2 (indicating that for every 1 unit increase in x, y increases by 2 units) and the y-intercept is 3 (which means the line crosses the y-axis at point (0, 3).
2. Standard Form: In mathematics, the standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants. The coefficients A and B should not have any common factors and A should be positive.
Illustration:
An example of a linear equation in standard form is 2x + 3y = 6. In this equation, A = 2, B = 3, and C = 6.
3. Point-Slope Form: This form of a linear equation is written as y - y₁ = m(x - x₁), where m represents the slope of the line and (x₁, y₁) represents a specific point on the line.
Illustration:
Given a point (2, 4) and a slope of 3, the equation of the line in point-slope form would be y - 4 = 3(x - 2).