Graph a line from an equation

Learning Objectives Identify the slope and y-intercept from a linear equation in slope-intercept form. Plot the y-intercept on a coordinate plane. Use the slope (rise over run) to find additional points on the line. Graph a linear equation by plotting at least two points and drawing a straight line through them. Rearrange a linear equation from standard form (Ax + By = C) into slope-intercept form (y = mx + b). Graph a linear equation by finding and plotting its x- and y-intercepts. Ever wonder how roller coasters are designed or how architects plan buildings? 🎢 Lines are everywhere, and understanding their equations helps us predict and create! In this lesson, you'll learn how to take a linear equation and visually represent it on a graph. This skill is fundamental f...

TermDefinitionExample Linear EquationAn equation whose graph is a straight line. It can be written in forms like y = mx + b or Ax + By = C.y = 2x + 3 Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis). Used for plotting points.The grid system where you plot points like (2, 5). Ordered PairA pair of numbers (x, y) that represents a single point on the coordinate plane, where x is the horizontal position and y is the vertical position.(3, -1) means 3 units right and 1 unit down from the origin. Slope (m)A measure of the steepness and direction of a line. It is calculated as 'rise over run' (change in y / change in x).In y = 2x + 3, the slope is m = 2, meaning for every 1 unit right, the line g...

Slope-Intercept Form $y = mx + b$ This form directly shows the slope ($m$) and the y-intercept ($b$). To graph, plot the y-intercept $(0, b)$, then use the slope $\frac{\text{rise}}{\text{run}}$ to find a second point. Standard Form of a Linear Equation $Ax + By = C$ This form is useful for finding the x- and y-intercepts. To find the x-intercept, set $y=0$ and solve for $x$. To find the y-intercept, set $x=0$ and solve for $y$. Plot these two intercepts and draw the line. Slope Formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ While not directly used to graph *from* an equation, this formula defines slope. Understanding it helps interpret $m$ in $y=mx+b$ as the change in y over the change in x between any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line.