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**4.2 Graphing Linear Equations**

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**Solution of a Linear Equation**

Is an ordered pair (x, y) that makes the equation true. Example: Determine whether the ordered pair is a solution of x + 2y = 5. a) (1, 2) b) (7, -3)

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**Writing Linear Equations in Slope-Intercept Form**

An equation is in slope intercept form when “y” is isolated (it is by itself on one side of the equal sign). y = mx + b

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**Example 2: Write the equation in slope – intercept form**

-2x + y = -3

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You Try It… Write each equation in slope-intercept form. Then identify the slope and the y-intercept. -3x + y = 12 2) 4y – 2x = 8 3) 5x + 2y + 15 = 0 4) -5x – 3y = 12

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**Graphs of Linear Equations**

The graph of an equation in x and y is the set of ALL points (x, y) that are solutions to the equation. The graph of a linear equation can be shown to be a straight line.

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**We can use Slope-Intercept form to Graph Equations**

Steps: 1) Write the equation in slope-intercept form (get “y” alone). 2) Identify slope (m) and y-intercept (b). 3) Plot the y-intercept. 4) Use the slope (rise/run) to plot at least 2 more points). 5) Connect all points with a straight line (USE A RULER!).

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**Example 3 Find the slope and y-intercept of y = -3x + 2**

Then graph the equation.

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**Example 4 Find the slope and y-intercept of 2x – y = -3**

Then graph the equation.

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**You Try It… Find the slope and y-intercept of each equation.**

Then graph the equation. y = -2x y = 4x – 5 y = x + 2

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Application Andrew has a small business making decorated hats. Based on data for the last eight months, he calculates his monthly cost y of producing x hats using the equation y = 1.9x A) Explain what the y-intercept and the slope mean in this model. B) graph the model. Then use the graph to estimate the cost of 35 hats.

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Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

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