Write a linear equation from a graph

Learning Objectives Identify key features of a linear graph, including points and intercepts. Calculate the slope (rate of change) of a line directly from its graph. Determine the y-intercept of a line from its graph. Write the equation of a line in slope-intercept form (y = mx + b) using information from its graph. Verify the correctness of a linear equation by checking additional points on the graph. Apply the process of writing linear equations from graphs to solve real-world problems. Ever wonder how scientists predict the path of a hurricane 🌀 or how much money you'll save each week if you put away a fixed amount? In this lesson, you'll learn how to translate a visual representation (a graph) into a powerful mathematical statement (a linear equation). This s...

TermDefinitionExample Linear EquationAn equation whose graph is a straight line. It describes a relationship where one quantity changes at a constant rate with respect to another.`y = 2x + 1` is a linear equation because its graph is a straight line. GraphA visual representation of data or a relationship between two variables, typically plotted on a coordinate plane.A line drawn on an x-y grid showing how temperature changes with altitude. Slope (m)A measure of the steepness and direction of a line. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.A line that goes up 3 units for every 2 units it goes right has a slope of `3/2`. Y-intercept (b)The point where a line crosses the y-axis. At this point, the x-coordinate is always...

Slope-Intercept Form of a Linear Equation `y = mx + b` This formula is used to write the equation of a straight line when you know its slope (`m`) and its y-intercept (`b`). Slope Formula (from two points) `m = \frac{y_2 - y_1}{x_2 - x_1}` This formula calculates the slope (`m`) of a line given any two distinct points `(x_1, y_1)` and `(x_2, y_2)` on the line.