Find the slope of a linear function

Learning Objectives Calculate the slope of a linear function given two distinct points. Determine the slope of a linear function from its graph by analyzing 'rise over run'. Identify the slope of a linear function when its equation is presented in slope-intercept form (f(x) = mx + b). Algebraically manipulate a linear equation from standard form (Ax + By = C) to find its slope. Interpret the slope as a rate of change in a real-world context. Differentiate between positive, negative, zero, and undefined slopes and describe the corresponding line's orientation. Have you ever wondered how engineers determine the steepness of a road or how economists track profit growth over time? 📈 They're all using the concept of slope! This tutorial will provide a deep d...

TermDefinitionExample Linear FunctionA function that can be represented by an equation of the form f(x) = mx + b. Its graph is a straight line.f(x) = 2x - 3 is a linear function. For every one-unit increase in x, the value of f(x) increases by two units. Slope (m)A measure of the steepness and direction of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two distinct points on the line.A slope of 3 means that for every 1 unit you move to the right on the x-axis, you must move 3 units up on the y-axis. Rate of ChangeDescribes how one quantity changes in relation to another quantity. For a linear function, the rate of change is constant and is equal to the slope.If a car travels at a constant 60 km/h, its rate of change of distance...

The Slope Formula m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x} Use this formula when you are given the coordinates of two points (x₁, y₁) and (x₂, y₂) on a line. Ensure that the order of subtraction is consistent for both the numerator and the denominator. Slope-Intercept Form f(x) = mx + b \quad \text{or} \quad y = mx + b When a linear function is written in this form, the slope is the coefficient 'm' of the x-term. The 'b' represents the y-intercept, the point where the line crosses the y-axis. Slope from Standard Form \text{For an equation } Ax + By = C, \text{ the slope is } m = -\frac{A}{B} \quad (\text{where } B \neq 0) This is a shortcut to find the slope when a linear equation is in standard form. Alternatively, you can alge...