then reload this page.
What do you think the graph of $4x+2y=4$ looks like? In this lesson you will learn about the
graph of this and other similar equations.
The slope of a line is a measurement of how steep it is. Use the figures
below to help remind you about how to measure the slope of a line. The
first line graphed below has slope $$3/2$$, while the second one has slope $$-3/2$$.
Look at the grid to the left to answer the following questions.
To the left is the graph of $Ax+By=C$.
You are looking at the graph of $4x+2y=4$
(because $A=4$, $B=2$, $C=4$). Use the sliders to change the values of $A$, $B$, and $C$ and
notice how each affects the shape and position of the graph of
Each row of the following table has a question about how the graph changes when you change
$A$, $B$, or $C$. Answer the question for each of the three variables.
The form $Ax+By=C$, where $A$, $B$, and $C$ are
constants, is called the standard form for
an equation for a line.
Use the sliders to set $A=4$, $B=2$, and $C=4$.
You are again looking at the graph of $4x+2y=4$. Slide the value of
$A$ toward zero.
Each row of the table below gives an equation for a line in standard form.
Using the sliders, change the values of $A$, $B$, and $C$, and complete this table. In each
case, find the slope of the line by looking at the grid to the left.
The slopes you have found suggest that:
The slope of the line $Ax+By=C$ is $$-A/B$$.
In the last question, you found the slopes of lines by looking at their graphs. If you want
to find the slope of a line algebraically, by using its
equation, you can convert that equation into slope-intercept form.
For example, we can write the equation $4x+2y=4$ in slope-intercept form as follows:
Each row of the table has an equation in standard form. Write that
equation in slope-intercept form.
The equations from convertQn have been summarized in the
table below. Use them to answer the following questions.
The $y$-intercept of a line is the point on that line where $x=0$, and the $x$-intercept is
the point where $y=0$. You can use this to find the intercepts of lines algebraically.
Algebraically find the $y$-intercept of each line in the table below.
Algebraically find the $x$-intercept of each line in the table below.