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Warm Up Find the slope of the line that passes through each pair of points. 1. (3, 6) and (–1, 4) 2. (1, 2) and (6, 1) 3. (4, 6) and (2, –1) 4. (–3, 0) and (–1, 1)

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**Learning Target #1 – write an equation in Slope-Intercept Form**

Learning Target #2 - to identify the pieces of a Slope-Intercept Equation Learning Target #3 - to use Slope-Intercept form to graph equations

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**You can graph a linear equation easily by finding the slope and the**

y-intercept. The slope of a line is the ratio of the rise to the run between two points and represents the slant of the graphed line. The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

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**In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.**

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Learning Targets #1 Write the equation that describes the line in slope-intercept form. slope = ; y-intercept = 4 y = mx + b Substitute the given values for m and b. Simply if necessary.

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**Write the equation that describes the line in slope-intercept form.**

slope = –9; y-intercept = y = mx + b Substitute the given values for m and b. Simply if necessary.

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**Write the equation that describes the line in slope-intercept form.**

slope = 2; (3, 4) is on the line Step 1 Find the y-intercept. y = mx + b Write the slope-intercept form. Substitute 2 for m, 3 for x, and 4 for y. Solve for b. Since 6 is added to b, subtract 6 from both sides to undo the addition.

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**Step 2 Write the equation.**

y = mx + b Write the slope-intercept form. Substitute 2 for m, and –2 for b.

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Check It Out! A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form.

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Learning Target #2 Write each equation in slope-intercept form, and then find the slope and y-intercept. 2x + y = 3 2x + y = 3 –2x –2x Subtract 2x from both sides. y = 3 – 2x Rewrite to match slope-intercept form. y = –2x + 3 The equation is in slope-intercept form. m = –2 b = 3 The slope of the line 2x + y = 3 is –2, and the y-intercept is 3.

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5y = 3x Divide both sides by 5 to solve for y. The equation is in slope-intercept form.

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4x + 3y = 9 Subtract 4x from both sides. Rewrite to match slope-intercept form. Divide both sides by 3. The equation is in slope-intercept form.

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5x + 4y = 8 Subtract 5x from both sides. Rewrite to match slope-intercept form. Divide both sides by 4. The equation is in slope-intercept form.

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Check It Out! Write each equation in slope-intercept form, and then find the slope and y-intercept. 4x + y = 4

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**Learning Target #3 - Using Slope-Intercept Form to Graph**

Write the equation in slope-intercept form. Then graph the line described by the equation. y = 3x – 1 y = 3x – 1 is in the form y = mx + b slope: m = 3 = y-intercept: b = –1 • Step 1 Plot (0, –1). • Step 2 Count 3 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

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**Write the equation in slope-intercept form**

Write the equation in slope-intercept form. Then graph the line described by the equation. 2y + 3x = 6 Step 1 Write the equation in slope-intercept form by solving for y. 2y + 3x = 6 Subtract 3x from both sides. Since y is multiplied by 2, divide both sides by 2.

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Step 2 Graph the line. is in the form y = mx + b. slope: m = y-intercept: b = Plot (0, ). • Count units down and units right and plot another point. • Draw the line connecting the two points.

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Check It Out! Write the equation in slope-intercept form. Then graph the line described by the equation. 6x + 2y = 10

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Application A closet organizer charges a $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.

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Application A closet organizer charges $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below. a. Write an equation that represents the cost as a function of the number of hours. Cost is $30 for each hour plus $100 y = 30 •x + 100 An equation is y = 30x

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**b. Identify the slope and y-intercept and describe their meanings.**

The y-intercept is 100. This is the cost for 0 hours, or the initial fee of $100. The slope is 30. This is the rate of change of the cost: $30 per hour. c. Find the cost if the organizer works 12 hrs. y = 30x + 100 Substitute 12 for x in the equation = 30(12) = 460 The cost of the organizer for 12 hours is $460.

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