Find the slope of an equation

Learning Objectives Define slope as the rate of change in a linear relationship. Calculate the slope of a line given two points on the line. Identify the slope of a line from its equation in slope-intercept form (y = mx + b). Rearrange a linear equation from standard form (Ax + By = C) into slope-intercept form to find its slope. Interpret the meaning of positive, negative, zero, and undefined slopes. Apply the concept of slope to real-world scenarios. Have you ever seen a ramp or a hill? ⛰️ How would you describe how steep it is? That 'steepness' is exactly what we're going to measure in math! In this lesson, you'll learn how to find the 'slope' of a line, which tells us how steep it is and in what direction it's going. Understanding slop...

TermDefinitionExample SlopeSlope is a measure of the steepness and direction of a line. It describes how much the vertical distance (rise) changes for every unit of horizontal distance (run).A road sign indicating a '6% grade' means the road rises 6 feet for every 100 feet horizontally, so its slope is 6/100. Linear EquationAn equation whose graph is a straight line. It represents a relationship where the rate of change (slope) is constant.y = 2x + 3 is a linear equation. When graphed, it forms a straight line. RiseThe vertical change between two points on a line. It's the change in the y-coordinates.If a point moves from y=2 to y=5, the rise is 3 units. RunThe horizontal change between two points on a line. It's the change in the x-coordinates.If a point moves from x=...

Slope Formula (from two points) $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Use this formula to calculate the slope (m) of a line when you are given the coordinates of two distinct points on the line, $(x_1, y_1)$ and $(x_2, y_2)$. Remember that $x_2 - x_1$ cannot be zero. Slope from Slope-Intercept Form $$y = mx + b$$ When a linear equation is written in slope-intercept form, the coefficient 'm' directly represents the slope of the line. 'b' represents the y-intercept. Slope from Standard Form To find the slope from $Ax + By = C$, first rearrange it to $y = mx + b$. This means isolating 'y': $By = -Ax + C \Rightarrow y = \frac{-A}{B}x + \frac{C}{B}$. The slope is $m = \frac{-A}{B}$. If your linear equation is in standard form, you must first so...