Graph a line using slope

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 at least two additional points on a line. Accurately draw a straight line through the plotted points. Graph a linear equation given in slope-intercept form ($y = mx + b$). Interpret the direction and steepness of a line based on its slope. Ever wonder how roller coasters are designed to go up and down at just the right angle? 🎢 It all comes down to understanding 'slope'! In this lesson, you'll learn a powerful method to draw straight lines on a graph using two key pieces of information: the slope and the y-intercept. This skill is fundamental for understanding how linear relat...

TermDefinitionExample Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points.The grid paper you use for graphing is a coordinate plane, with the point (0,0) at its center. Linear EquationAn equation whose graph is a straight line. It typically involves two variables, like x and y, raised to the first power.$y = 2x + 3$ is a linear equation. Slope (m)A measure of the steepness and direction of a line. It describes how much the line rises or falls vertically for every unit it moves horizontally.A slope of 2 means the line goes up 2 units for every 1 unit it goes right. Y-intercept (b)The point where a line crosses the y-axis. At this point, the x-coordinate is always 0.In the equation $y = 2x +...

Slope-Intercept Form $y = mx + b$ This is the standard form for a linear equation where 'm' represents the slope of the line and 'b' represents the y-intercept (the point where the line crosses the y-axis, (0, b)). Slope Formula (Rise over Run) $m = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}$ This formula defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line. A positive slope means the line goes up from left to right, and a negative slope means it goes down.