Do Now 11/15/11 Line 1: (2, -7) (0,-5) Line 2 (0, 4), (8, 3.5)

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Presentation transcript:

Do Now 11/15/11 Line 1: (2, -7) (0,-5) Line 2 (0, 4), (8, 3.5) In your notebook, explain how you find the equation for a line when given two points. Then find the equation of the following two lines. Line 1: (2, -7) (0,-5) Line 2 (0, 4), (8, 3.5) y = -x – 5 y = -1/16x + 4

Objective write equations of lines using points on the line.

Section 5.2 “Use Linear Equations in Slope-Intercept Form” a linear equation written in the form y-coordinate x-coordinate y = mx + b slope y-intercept

Writing an Equation Using Slope-Intercept Form Step #1 Identify slope. Step #2 Find the y-intercept. Substitute the slope and the coordinates of a point (x,y) on the line y = mx + b. Then solve for b. Step #3 Write the equation using y = mx + b

Write an equation of the line that passes through the point (– 1, 3) and has a slope of – 4. STEP 1 Identify the slope. The slope is – 4. STEP 2 Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x + b. Solve for b. y = m x + b Write slope-intercept form. 3 = – 4(– 1) + b Substitute – 4 for m, – 1 for x, and 3 for y. – 1 = b Solve for b. STEP 3 Write an equation of the line. y = m x + b Write slope-intercept form. y = – 4x – 1 Substitute – 4 for m and – 1 for b.

Write an equation of the line that passes through the point (6, 3) and has a slope of 2. STEP 1 Identify the slope. The slope is 2. STEP 2 Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x + b. Solve for b. y = m x + b Write slope-intercept form. 3 = 2(6 ) + b Substitute 2 for m, 6 for x, and 3 for y. – 9 = b Solve for b. STEP 3 Write an equation of the line. y = m x + b Write slope-intercept form. y = 2x – 9 Substitute 2 for m and – 9 for b.

Write an equation of the line that passes through (– 2, 5) and (2, – 1). STEP 1 Calculate the slope. 3 m = y2 – y1 x2 – x1 = – 1 – 5 2 – (– 2) – 6 4 – 2 STEP 2 Find the y-intercept. Use the slope and the point (-2, 5). Solve for b. y = m x + b Write slope-intercept form. 5 = – 3 2 (– 2) + b Substitute – for m, – 2 for x, and 5 for y. 3 2 2 = b Solve for b. STEP 3 Write an equation of the line. y = m x + b Write slope-intercept form. y = – 3 2 x + 2 Substitute – 3 2 for m and 2 for b.

Write an equation of the line that passes through (1, 4) and (2, 7). STEP 1 Calculate the slope. 3 m = y2 – y1 x2 – x1 = 7 – 4 2 – 1 1 STEP 2 Find the y-intercept. Use the slope and the point (2, 7). Solve for b. y = m x + b Write slope-intercept form. 7 = 3 1 ( 2) + b Substitute for m, 2 for x, and 7 for y. 3 1 1 = b Solve for b. STEP 3 Write an equation of the line. y = m x + b Write slope-intercept form. y = 3 1 x + 1 Substitute 3 1 for m and 1 for b.

Slope-Intercept Form Summary When given: (1) slope and y-intercept Substitute into equation (2) slope and one point Substitute m and the coordinates of the point in y = mx + b. Then solve for b. (3) two points Use the 2 points to find the slope. Then substitute m and the coordinates of the point in y = mx + b. Then solve for b.

With your tribe, work on the “Real-Life” applications Bald Eagle worksheet.

Algebra in “Real-Life!” In your groups, complete the two “real-life” activities. Interdisciplinary Application “Bald Eagles” 1) y = 393x + 14,324 2) graph 3) approximately 18,254 4) habitat loss, less people counting 5) y = 512.25x + 13,698 6) graph 7) approximately 18,880