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**1.2: Graphs of Equations 1.3: Linear Equations**

Objectives: To find the intercepts of a graph To use symmetry as an aid to graphing To write the equation of a circle and graph it To write equations of parallel and perpendicular lines

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Vocabulary As a class, use your vast mathematical knowledge to define each of these words without the aid of your textbook. Graph of an Equation Solution Point Intercepts Symmetry Circle Parallel Perpendicular

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Graph of an Equation The graph of an equation gives a visual representation of all solution points of the equation.

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Intercepts The x-intercept of a graph is where it intersects the x-axis. (a, 0) The y-intercept of a graph is where it intersects the y-axis. (0, b)

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Exercise 1 How many x- and y-intercepts can the graph of an equation have? How about the graph of a function?

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Exercise 2 Given an equation, how do you find the intercepts of its graph? To find the x-intercepts, set y = 0 and solve for x. To find the y-intercepts, set x = 0 and solve for y.

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Exercise 3 Find the x- and y-intercepts of y = – x2 – 5x.

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Symmetry A figure has symmetry if it can be mapped onto itself by reflection or rotation. Click me!

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Exercise 4 How would an understanding of symmetry help you graph an equation?

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**Symmetry When it comes to graphs, there are three basic symmetries:**

x-axis symmetry: If (x, y) is on the graph, then (x, -y) is also on the graph.

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**Symmetry When it comes to graphs, there are three basic symmetries:**

y-axis symmetry: If (x, y) is on the graph, then (-x, y) is also on the graph.

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**Symmetry When it comes to graphs, there are three basic symmetries:**

Origin symmetry: If (x, y) is on the graph, then (-x, -y) is also on the graph. (Rotation of 180)

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Exercise 5 Using the partial graph pictured, complete the graph so that it has the following symmetries: x-axis symmetry y-axis symmetry origin symmetry

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Circle The set of all coplanar points is a circle if and only if they are equidistant from a given point in the plane.

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Exercise 6 Find the equation of points (x, y) that are r units from (h, k).

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**Equation of a Circle Standard form of the equation of a circle:**

(h, k) = center point r = radius

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Exercise 7 The point (1, -2) lies on the circle whose center is at (-3, -5). Write the standard form of the equation of the circle.

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Exercise 8 Find the center and radius of the circle, and then sketch the graph.

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**Linear Equations (Again)**

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**Exercise 9 Convert the given equation to the following forms:**

Slope-intercept form Standard form

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**Exercise 10 Convert the given equation to the following forms:**

Slope-intercept form Point-slope form

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**Parallel and Perpendicular**

Two lines are parallel lines iff they are coplanar and never intersect. Two lines are perpendicular lines iff they intersect to form a right angle. m || n

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**Parallel and Perpendicular**

Two lines are parallel lines iff they have the same slope. Two lines are perpendicular lines iff their slopes are negative reciprocals.

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Example 11 Write an equation of the line that passes through the point (-2, 1) and is: Parallel to the line y = -3x + 1 Perpendicular to the line y = -3x + 1

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**1.2: Graphs of Equations 1.3: Linear Equations**

Objectives: To find the intercepts of a graph To use symmetry as an aid to graphing To write the equation of a circle and graph it To write equations of parallel and perpendicular lines

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