In this Grade 9 Saxon Algebra 1 lesson, students learn how to find x-intercepts and y-intercepts of linear equations by substituting zero for each variable, and use those intercepts to graph lines on a coordinate plane. The lesson covers the standard form of a linear equation (Ax + By = C) and demonstrates how to convert equations into standard form before identifying intercepts. Students also practice reading intercepts directly from graphs and applying the intercept method to real-world problems involving linear relationships.
Section 1
š Locating and Using Intercepts
The -intercept is the -coordinate where a graph crosses the -axis. The -intercept is the -coordinate where a graph crosses the -axis.
Next, you'll practice finding intercepts algebraically by substituting zero values. Soon, we'll explore worked examples with standard form equations and challenge problems using intercepts in real applications.
Section 2
Standard Form of a Linear Equation
The standard form of a linear equation is , where , and are real numbers and and are not both zero.
To write in standard form, add to both sides to get .
To write in standard form, subtract from both sides to get .
Think of standard form as tidying up your equation! It neatly puts both variables on one side and the constant on the other. This setup makes it super easy to find the intercepts and graph the line, getting all the messy parts organized before you start solving.
Section 3
Finding x- and y-intercepts
The -intercept is the -coordinate where the graph intersects the -axis (so ). The -intercept is the -coordinate where the graph intersects the -axis (so ).
For , set to get , so the -intercept is 10.
For , set to get , so the -intercept is 8.
Intercepts are a line's 'touchdown' points on the axes! To find where the line hits the x-axis, you can't have any 'up or down' movement, so set . To find where it hits the y-axis, you can't have any 'left or right' movement, so set .
Section 4
Graphing Using Intercepts
An efficient method for graphing a linear equation in two variables is to plot the - and -intercepts and then to draw a line through them.
To graph , first find the intercepts.
The -intercept is and the -intercept is .
Plot the points and and draw a straight line through them.
Why do more work than you need to? Finding the two intercepts gives you the two points required to define a straight line. Just plot those two special points on the axes and connect them with a ruler. It's the fastest way to accurately graph a linear equation!
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Section 1
š Locating and Using Intercepts
The -intercept is the -coordinate where a graph crosses the -axis. The -intercept is the -coordinate where a graph crosses the -axis.
Next, you'll practice finding intercepts algebraically by substituting zero values. Soon, we'll explore worked examples with standard form equations and challenge problems using intercepts in real applications.
Section 2
Standard Form of a Linear Equation
The standard form of a linear equation is , where , and are real numbers and and are not both zero.
To write in standard form, add to both sides to get .
To write in standard form, subtract from both sides to get .
Think of standard form as tidying up your equation! It neatly puts both variables on one side and the constant on the other. This setup makes it super easy to find the intercepts and graph the line, getting all the messy parts organized before you start solving.
Section 3
Finding x- and y-intercepts
The -intercept is the -coordinate where the graph intersects the -axis (so ). The -intercept is the -coordinate where the graph intersects the -axis (so ).
For , set to get , so the -intercept is 10.
For , set to get , so the -intercept is 8.
Intercepts are a line's 'touchdown' points on the axes! To find where the line hits the x-axis, you can't have any 'up or down' movement, so set . To find where it hits the y-axis, you can't have any 'left or right' movement, so set .
Section 4
Graphing Using Intercepts
An efficient method for graphing a linear equation in two variables is to plot the - and -intercepts and then to draw a line through them.
To graph , first find the intercepts.
The -intercept is and the -intercept is .
Plot the points and and draw a straight line through them.
Why do more work than you need to? Finding the two intercepts gives you the two points required to define a straight line. Just plot those two special points on the axes and connect them with a ruler. It's the fastest way to accurately graph a linear equation!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter