Section 3.5 ~ Write and Graph Linear Equations
Topics in this lesson:
• slope­intercept form
• standard form
• x and y intercepts
• writing equations for lines
Vocabulary
slope­intercept form ­ y = mx + b where m is the slope and b is the y­intercept
standard form ­ Ax + By = C y­intercept ­ the point where a line crosses the y­axis x­intercept ­ the point where a line crosses the x­axis
We need to know how to write linear equations given different kinds of information.
Example 1 ­ When a graph is given
Step 1: Find the slope. Step 2: Find the y­intercept.
Step 3: Fill in the blanks: y = ____x + ____
m
3.5
b
1
Example 2 ­ When a parallel line and point are given
Write an equation of the line passing through the point (1, ­1) that is parallel to the line with the equation y = 2x ­ 1.
Step 1: Find the slope.
Step 2: Find the y­intercept by plugging in your m, x, and y to y = mx + b.
Step 3: Fill in the blanks: y = ____x + ____
m
b
Example 3 ­ When a perpendicular line and point are given
Write an equation of the line j passing through the point (3, 2) that is perpendicular to the line k with the equation y = ­3x + 1.
Step 1: Find the slope.
Step 2: Find the y­intercept by plugging in your m, x, and y to y = mx + b.
Step 3: Fill in the blanks: y = ____x + ____
m
3.5
b
2
Example 4 ­ Given a graph of a real­life situation
The graph models the total cost of renting an apartment. Write an equation of the line. Explain the meaning of the slope and the y­intercept of the line.
Step 1: Find the slope.
Step 2: Find the y­intercept.
Step 3: Fill in the blanks: y = ____x + ____
m
b
Step 4: Explain the equation.
The equation y = _________________ models the _________________.
The slope is ___________________________________.
The y­intercept is _____________________________________.
Example 5
The equation y = 650x + 425 models the total cost of joining a health club for x years. What are the meaning of the slope and y­intercept of the line? slope = y­intercept = What would it cost to join and remain a member for 5 years?
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3
We also need to know how to graph lines given their linear equation.
Example 6 ­ Graph y = 3x + 1
Step 1: Plot the y­intercept.
Step 2: Count off the slope from the y­intercept to get a second point on the line.
Step 3: Connect the points.
Example 7 ­ Graph 2x + 3y = 6
This equation is in standard form. Rewrite it in slope­intercept form and follow steps above.
Example 8 ­ Graph y = 3 and x = 4. In the equation y = 3, y always equals 3.
What line makes that true? In the equation x = 4, x always equals 4.
What line makes that true?
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4
Intercepts
The y­intercept is the point where a line crosses the y­axis. The x­intercept is the point where a line crosses the x­axis. The x­value in any y­intercept is 0, so to find a y­intercept, set x in the equation = to 0 and solve.
The y­value in any x­intercept is 0, so to find a x­intercept, set y in the equation = to 0 and solve.
Example 9 ­ Find the x and y intercepts of 2x + 3y = 6.
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5