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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

2. Reflections

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Exercise 33 Page 557

You only need to reflect two points on the line y=3x+2 to draw the image.

y=- 3x-4

Practice makes perfect

Let's draw y=3x+2 and the line of reflection y=- 1 in the same coordinate plane.

To reflect y=3x+2 in y=- 1, we only need two points.

Now we can connect the reflected points with a line to have the new image.

To find the new equation, we have to determine its slope and y-intercept. From the diagram, we can already see that the y-intercept is - 4. Therefore, we can write the equation so far as y=mx-4 To find the line's slope, we use the Slope Formula.

m = y_2 - y_1/x_2 - x_1

SubstitutePoints

Substitute ( - 2,2) & ( 1,- 7)

m = - 7 - 2/1 - ( - 2)

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Simplify right-hand side

a-(- b)=a+b

m = - 7 - 2/1 + 2

Add and subtract terms

m = - 9/3

Calculate quotient

m = - 3

Finally, we can write the equation of the image in slope-intercept form. y=- 3x-4

Subchapter links

Communicate Your Answer p.551

Monitoring Progress p.552-555

Exercises p.556-558