Write a linear equation from a slope and a point

Learning Objectives Identify the slope and a given point from a problem description. Recall and apply the point-slope form of a linear equation. Substitute given slope and point coordinates into the point-slope form. Algebraically manipulate the point-slope form into the slope-intercept form ($y = mx + b$). Write the final linear equation in slope-intercept form. Verify their derived equation by substituting the given point. Ever wonder how engineers predict the path of a rocket 🚀 or how economists model sales trends? It all starts with understanding how to describe a straight line! In this lesson, you'll learn a powerful skill: how to write the equation of a straight line when you know its steepness (slope) and just one point it passes through. This is a fundamental...

TermDefinitionExample Linear EquationAn equation whose graph is a straight line. It shows a constant rate of change between two variables.$y = 2x + 5$ Slope (m)A measure of the steepness and direction of a line. It represents the 'rise over run' or the change in $y$ divided by the change in $x$.If a line rises 3 units for every 1 unit it moves to the right, its slope is $m = 3$. Point ($x_1, y_1$)A specific location on a coordinate plane, represented by an ordered pair of numbers.The point $(2, 7)$ means $x=2$ and $y=7$. Y-intercept (b)The point where a line crosses the y-axis. At this point, the x-coordinate is always 0.In $y = 2x + 5$, the y-intercept is $(0, 5)$, so $b=5$. Slope-Intercept FormA common way to write linear equations, where $y$ is isolated, making the slope ($m$...

Slope-Intercept Form $y = mx + b$ This form is used to represent a linear equation where 'm' is the slope and 'b' is the y-intercept. Our goal is often to get the equation into this form. Point-Slope Form $y - y_1 = m(x - x_1)$ This is the primary formula we use when given a slope 'm' and a specific point '($x_1, y_1$)'. You substitute the given values into this formula, then rearrange it into slope-intercept form.