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Writing Equations in Point-Slope Form Lesson 4 -3

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.

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

Write and Graph an Equation in Point-Slope Form 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. Answer:

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

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

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

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

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

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

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

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.

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

Point-Slope Form and Standard Form Step 2 You 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)

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

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

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

Homework Page 236 #11 – 49 odd