TL1 Equations of Lines - MTH 121 Spring 2026

Core Concepts¶

In order to define a line in the $xy$ -plane we need two things: a point that sits on the line and the slope of the line.

Starting Point and Direction: It is helpful to think of the given point as the place to start drawing the line and the slope as the direction it should be drawn in.

Properties of Slope¶

Positive slope, zero slope, negative slope
Parallel Lines have the same slope.
Perpendicular Lines have slopes which are negative reciprocals of each other.

Finding the Line Equation¶

Given a point on the line and the slope, we should use the point slope formula to find the equation of the line.
Given two points on the line, we should first find the slope and then, to get the actual equation of the line, use the point slope formula.

Important Equations¶

Slope Formula

m= \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{\Delta y}{\Delta x}

Point Slope Formula

(y-y_c)=m(x-x_c)

Slope-Intercept Formula

y=mx+b

Intro Examples¶

Primary Examples¶

Homework¶

Write out each question as well as your solution on the homework page template.

Make sure you leave a good amount of blank space between each question.