Download 2 - Mira Costa High School

2.3 Graph Equations of Lines
Goal  Graph linear equations in slope-intercept or standard form.
Your Notes
VOCABULARY
Parent function
The most basic function in a family of functions
y-intercept
The y coordinate of a point where the graph intersects the y - axis
Slope-intercept form
An equation of the form y= mx + b with slope m and y - intercept b
Standard form of a linear equation
The standard form of a linear equation is Ax + By= C where A and B are not both zero.
x-intercept
The coordinate of a point where a graph intersects the x – axis
PARENT FUNCTION FOR LINEAR FUNCTIONS
The parent function for the family of all linear functions is y = __x_. The graph of y = x is
shown.
In general, a y- intercept of a graph is the y - coordinate of a point where the graph
intersects the y-axis.
Your Notes
USING SLOPE-INTERCEPT FORM TO GRAPH AN EQUATION
Step 1 Write the equation in __slope-intercept__ form by solving for y.
Step 2 __Identify__ the y-intercept b and use it to plot the point (0, b) where the line
crosses the y -axis.
Step 3 Identify the __slope__ m and use it to plot a second point on the line.
Step 4 __Draw__ a line through the two points.
Example 1
Graph an equation in slope-intercept form
Graph y = 
3
x + 1.
2
Step 1 The equation is already in slope-intercept form.
Step 2 The y-intercept is __1__ , so plot the point (__0__,__1__) where the line crosses
the__ y – axis__.
3
-3

,so plot a second point on the line by starting at
2
Step 3 The slope is ______
or
2
(__0,1__) and then moving down _3_ units and right _2_ units. The second point
is (__2,2__).
Step 4 Draw a line through the two points.
USING STANDARD FORM TO GRAPH AN EQUATION
Step 1 Write the equation in standard form.
Step 2 Identify the x-intercept by letting __y_ = 0 and solving for __x__. Use the xintercept to plot the point where the line crosses the x – axis.
Step 3 Identify the y-intercept by letting __x__ = 0 and solving for __y__. Use the yintercept to plot the point where the line crosses the __y – axis__.
Step 4 Draw a line through the two points.
Your Notes
Example 2
Graph an equation in standard form
Graph 2x + 3y = 12.
Solution
Step 1 The equation is already in standard form.
Step 2
2x + 3(__0__) = 12
Let y = __0__
x=6
Solve for x.
Plot the x-intercept at (__6__,0).
Step 3
2(__0__) + 3y = 12
Let x = __0__.
y = __4__
Solve for y.
Plot the y-intercept at (0,__4__).
Step 4 Draw a line through the two points.
HORIZONTAL AND VERTICAL LINES
Horizontal lines The graph of y = c is the horizontal line through (__0__,__c__).
Vertical lines The graph of x = c is the vertical line through (__c__,__0__).
Example 3
Graph horizontal and vertical lines
a. Graph y = 1
b. Graph x = 2.
Solution
a. The graph of y = 1 is the __horizontal__ line that passes through the point (0,_1__).
Notice that every point on the line has a y-coordinate of 1_.
b. The graph of x = 2 is the __vertical__ line that passes through the point (__2_,0).
Notice that every point on the line has an x-coordinate of __2__.
Your Notes
Checkpoint Graph the equation.
1. y = 2x + 2
2. y =
4
x 4
3
3. 4x + 2y = 8
4. 5x + 3y = 15
5. y = 4
6. x = 2
Homework
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