Splash Screen. Then/Now You wrote linear equations given either one point and the slope or two points. Write equations of lines in point-slope form. Write.

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Presentation transcript:

Splash Screen

Then/Now You wrote linear equations given either one point and the slope or two points. Write equations of lines in point-slope form. Write linear equations in different forms.

Vocabulary point-slope form

Concept 1

Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation for a line that passes through (–2, 0) with slope Simplify.

Example 1 Write and Graph an Equation in Point-Slope Form Answer: Graph the equation Plot the point at (–2, 0). Use the slope to find another point on the line. Draw a line through the two points.

Example 1 A.y – 4 = –2(x + 3) B.y + 3 = –2(x – 4) C.y – 3 = –2(x – 4) D.y + 4 = –2(x – 3) Write the point-slope form of an equation for a line that passes through (4, –3) with a slope of –2.

Concept 2

Example 2 In standard form, the variables are on the left side of the equation. A, B, and C are all integers. Multiply each side by 4 to eliminate the fraction. Original equation Distributive Property Writing an Equation in Standard Form

Example 2 Writing an Equation in Standard Form 4y – 3x = 3x – 20 – 3x –3x + 4y = –20 Answer: The standard form of the equation is 3x – 4y = 20. Simplify. Subtract 3x from each side. 3x – 4y = 20Multiply each side by –1.

Example 2 A.–2x + y = 5 B.–2x + y = 11 C.2x – y = –11 D.2x + y = 11 Write y – 3 = 2(x + 4) in standard form.

Example 3 Writing an Equation in Slope-Intercept Form Distributive Property Original equation Add 5 to each side.

Example 3 Writing an Equation in Slope-Intercept Form Simplify. Answer: The slope-intercept form of the equation is

Example 3 Write 3x + 2y = 6 in slope-intercept form. A. B.y = –3x + 6 C.y = –3x + 3 D.y = 2x + 3

Example 4 Point-Slope Form and Standard Form A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD. Write an equation in point-slope form for the line containing the side BC. ___

Example 4 Point-Slope Form and Standard Form Step 1Find the slope of BC. Slope formula (x 1, y 1 ) = (4, 3) and (x 2, y 2 ) = (6, –2)

Example 4 Point-Slope Form and Standard Form Step 2You can use either point for (x 1, y 1 ) in the point-slope form. Using (4, 3) Using (6, –2) y – y 1 = m(x – x 1 )

Example 4 Point-Slope Form and Standard Form B. Write an equation in standard form for the same line. Answer: 5x + 2y = 26 Original equation Distributive Property Add 3 to each side. Multiply each side by 2. Add 5x to each side. 2y = –5x x + 2y = 26

Example 4 A.y – 6 = 1(x – 4) B.y – 1 = 1(x + 3) C.y + 4 = 1(x + 6) D.y – 4 = 1(x – 6) A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.

Example 4 A.–x + y = 10 B.–x + y = 3 C.–x + y = –2 D.x – y = 2 B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.

End of the Lesson