Graph a linear equation (Tutorial Only)

Learning Objectives Graph a linear equation given in slope-intercept form. Graph a linear equation given in standard form by finding the x- and y-intercepts. Graph a linear equation given in point-slope form. Identify and graph special cases, including horizontal and vertical lines. Determine the slope and y-intercept of a line from its graph. Convert a linear equation from standard or point-slope form to slope-intercept form to facilitate graphing. Ever wondered how your phone calculates its remaining battery life or how GPS estimates your arrival time? 📱 It all starts with the simple, powerful concept of a straight line! This tutorial will guide you through the process of visually representing linear equations on the coordinate plane. We will explore three primary method...

TermDefinitionExample Coordinate PlaneA two-dimensional grid formed by two perpendicular number lines, the horizontal x-axis and the vertical y-axis. It's the canvas on which we graph equations.The point (2, -3) is located by moving 2 units to the right of the origin and 3 units down. Linear EquationAn equation whose graph is a straight line. It represents a constant rate of change between two variables, typically x and y.y = 3x + 2 is a linear equation. For every one-unit increase in x, y increases by three units. Slope (m)A number that measures the steepness and direction of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.A slope of m = -2/3 means the line goes down 2 units for every 3 units it mo...

Slope-Intercept Form y = mx + b This is the most common form for graphing. 'm' represents the slope of the line, and 'b' represents the y-coordinate of the y-intercept (0, b). Use this form to plot the y-intercept first, then use the slope to find a second point. Standard Form Ax + By = C In this form, A, B, and C are integers. This form is particularly useful for quickly finding the x- and y-intercepts of the graph. To find the x-intercept, set y=0 and solve for x. To find the y-intercept, set x=0 and solve for y. Point-Slope Form y - y₁ = m(x - x₁) This form is used when you know the slope 'm' and any single point (x₁, y₁) on the line. To graph from this form, plot the known point (x₁, y₁) and then use the slope 'm' to find a...