Section 2.5
Equations of Lines and Linear Models
Example 1: Find the slope and y-intercept of the line with equation 4𝑥 + 5𝑦 = −10.
Section 2.5 Equations of Lines and linear Models
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Example 2: Write an equation of the line through (−4, 1) having slope −3. Write the
result in the slope-intercept form.
Example 3: Write an equation of the line through (1, 1) and (2, 4). Then graph the
line using the slope-intercept form.
Section 2.5 Equations of Lines and linear Models
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Standard form
The Standard form of the line is 𝑨𝒙 + 𝑩𝒚 = 𝑪, where A, B, and C are integers with
A > 0. The form must be written in the simplest form.
Example 4: Write an equation of the line through (−3, 2) and (2, −4). Write the
result in the standard form 𝐴𝑥 + 𝐵𝑦 = 𝐶.
Example 5: Use the graph of the linear function
𝑓 shown on the right to complete the following.
a) Find the slope, 𝑦-intercept, and 𝑥-intercept.
b) Write the equation that defines 𝑓.
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Example 6:
a) Write an equation of the vertical line through the point (2, 7).
b) Write an equation of the horizontal line through the point (2, 7).
c) Write an equation of the line through the point (−1, 3) and (−1, −2).
d) Write an equation of the line through the point (−1, 3) and (2, 3).
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Example 7: Write the equation in both slope-intercept and standard form of the line
that passes through the point (6, 2) and satisfies the given condition.
a) parallel to the line 2𝑥 + 3𝑦 = 4.
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b) perpendicular to the line 𝑥 + 2𝑦 = 4.
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Example 8: Graph the following linear functions, and find the domain and the range.
a. 𝒙 = −𝟐
b. 𝒚 = 𝟒
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