Algebra 1/Unit 6: X-intercepts and Y-intercepts, Slopes
![]() |
Subject classification: this is a mathematics resource. |
![]() |
Educational level: this is a secondary education resource. |
![]() |
Type classification: this is a lesson resource. |
Algebra 1/Unit 6: X-intercepts, Y-intercepts, and Slopes
Welcome to Week 6 of the Algebra 1 Course. This week, we will focus on:
- What it means to find the x-intercept(s) and y-intercept(s) of a linear equation
- How to identify the slope of a line (using a graph or algebraic formula)
- Tips on interpreting these concepts for straight-line equations
Introduction
[edit | edit source]By now, you know how to plot linear equations by finding a few points and drawing a line. However, there are more straightforward techniques for specific tasks, like finding:
- The x-intercept: where a line crosses the x-axis (i.e., where ).
- The y-intercept: where a line crosses the y-axis (i.e., where ).
- The slope: which measures the “steepness” or inclination of the line.
We will explore each of these ideas in detail.
X-intercept
[edit | edit source]A line’s x-intercept is the point at which the line crosses the x-axis. At any point on the x-axis,
Finding the x-intercept from an equation
[edit | edit source]If you have a linear equation in terms of and , you can find its x-intercept by:
- Substituting into the equation
- Solving for
Example (X-intercept from standard form) Suppose we have
- Let . The equation becomes This is the same as
- Solve for :
Therefore, the x-intercept is the point .
Y-intercept
[edit | edit source]A line’s y-intercept is the point at which the line crosses the y-axis. At any point on the y-axis,
Finding the y-intercept from an equation
[edit | edit source]If you have a linear equation in terms of and , you can find its y-intercept by:
- Substituting into the equation
- Solving for .
Example (Y-intercept from slope-intercept form) If the line is given by :
- Let . That gives
Hence, the y-intercept is .
Slope of a Line
[edit | edit source]The slope of a line measures how steep the line is and the direction it moves. For two points on a line, say and , the slope is:
If an equation is in the slope-intercept form , then (the coefficient of ) is the slope, and is the y-intercept.
Key Slope Types
[edit | edit source]- **Positive slope**: The line goes up as you move from left to right (i.e. the value increases as the value increases)
- **Negative slope**: The line goes down as you move from left to right (i.e. the value decreases as the value increases).
- **Zero slope**: The line is perfectly horizontal (). This also means that all values are 0.
- **Undefined slope**: The line is vertical (), and the slope formula would have a zero denominator.
Examples
[edit | edit source]Example 1: Find the x-intercept, y-intercept, and slope
[edit | edit source]Let’s use the equation
- **Y-intercept**: Let . Then . So y-intercept is .
- **X-intercept**: Let . Then → → . So x-intercept is .
- **Slope**: The coefficient of is . So .
Example 2: Use two points to find slope
[edit | edit source]Suppose a line passes through and . Find its slope.
- Using :
Therefore, the slope is , indicating the line goes down 1 unit for every 1 unit you move to the right.
Practice Problems
[edit | edit source]- For the equation :
- Find the x-intercept.
- Find the y-intercept.
- Rewrite the equation in slope-intercept form to identify the slope.
- A line goes through the points and . Find its slope. Is it positive, negative, or zero?
- Given , is there an x-intercept? Explain what the graph looks like and how that relates to slope.
- Bonus: If a line is described by , what is its slope? Does it have a y-intercept?