Write a linear equation from two points

Learning Objectives Define and identify key components of a linear equation. Accurately calculate the slope of a line given any two points. Use the slope and one point to find the y-intercept (b) of a linear equation. Write a linear equation in slope-intercept form ($y = mx + b$) given two points. Verify their derived linear equation by substituting the given points. Understand that two distinct points uniquely define a straight line. Ever wonder how meteorologists predict weather patterns or how engineers design roller coasters? 🎢 Many real-world situations can be described by straight lines! In this lesson, you'll learn a powerful skill: how to write the equation of a straight line just by knowing two points on that line. This is super important because it allows us...

TermDefinitionExample Linear EquationAn equation whose graph is a straight line. It shows a relationship where a change in one variable results in a proportional change in another.$y = 2x + 3$ is a linear equation. If you plot all the points that satisfy this equation, they form a straight line. Slope (m)The steepness of a line, often described as 'rise over run'. It tells us how much the y-value changes for every unit change in the x-value.If a line goes up 3 units for every 1 unit it moves to the right, its slope is $m = 3/1 = 3$. Y-intercept (b)The point where a line crosses the y-axis. At this point, the x-coordinate is always 0.In the equation $y = 2x + 3$, the y-intercept is 3, meaning the line crosses the y-axis at the point $(0, 3)$. Slope-Intercept FormA common way to w...

Slope Formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ Use this formula to calculate the slope (m) of a line when you are given two distinct points $(x_1, y_1)$ and $(x_2, y_2)$. Remember that $x_1 \neq x_2$ for a defined slope. Slope-Intercept Form of a Linear Equation $y = mx + b$ This is the standard form for a linear equation. Once you find the slope (m) and the y-intercept (b), you can write the complete equation of the line. You can find 'b' by substituting a known point $(x, y)$ and the calculated 'm' into this equation and solving for 'b'.