Do Now 6/10/10 Take out HW from last night. Take out HW from last night. –Text p. 411, #1-10 all Copy HW in your planner. Copy HW in your planner. –Text p. 422, #8-22 even, #15 & #21 In your notebook, answer the following question. Can you write an equation for the line on the graph? In your notebook, answer the following question. Can you write an equation for the line on the graph?

Homework Text p. 411, #1-10 all 1) parallel 1) parallel 2) perpendicular 2) perpendicular 3) perpendicular 3) perpendicular 4) parallel 4) parallel 5) no; they lie in the same line. 5) no; they lie in the same line. 6) no; they intersect 6) no; they intersect 7) yes; they do not lie in the same plane and do not intersect 7) yes; they do not lie in the same plane and do not intersect 8) lines AG, CE, EF 8) lines AG, CE, EF 9) lines BD, EG 9) lines BD, EG 10) lines HJ, EG 10) lines HJ, EG

Objective SWBAT write linear equations SWBAT write linear equations

Section 8.6 “Writing Linear Equations” SLOPE-INTERCEPT FORM- a linear equation written in the form y = mx + b slope y-intercept y-coordinatex-coordinate You can write a linear equation in slope- intercept form, if you know the slope (m) and the y-intercept (b) of the equation’s graph.

Slope Review The slope m of a line passing through two points and is the ratio of the rise change to the run. and is the ratio of the rise change to the run. y x run rise

The graph crosses the y-axis at (0, 2). The y-intercept is 2. Write an equation of the line shown. y = mx + b The slope of the line is a rise of 2 and a run of 4. The slope is 1/2. y = ½x + 2

The graph crosses the y-axis at (0, -1). The y-intercept is -1. Write an equation of the line shown. y = mx + b The slope of the line is a rise of 1 and a run of 2. The slope is 1/2. y = ½x – 1

y = mx + b y = x – Substitute for m and 5 for b. 4 3 – STEP 1 Write an equation of the line. The line crosses the y -axis at (0, – 5). So, the y- intercept is – 5. x 2 – x – 0 y 2 – y 1 = m = – 1 – (– 5) = 4 Write slope-intercept form. Calculate the slope. STEP 2 Write an equation of the line that passes through the given points. (3, -1), (0, -5)

Write an equation of the line that passes through the given points. (-6, 0), (0, -24) Calculate the slope of the line that passes through (-6, 0) and (0, -24). x 2 – x 1 -6 – 0 y 2 – y 1 = m = 0 – (-24) = = -4 STEP 1 y = mx + b Write slope-intercept form. y = -4x + (-24) Substitute -4 for m and -24 for b. Write an equation of the line. The line crosses the y -axis at (0, -24). So, the y- intercept is -24. STEP 3 The equation is y = -4x – 24.

Write an equation of the line that passes through the given points (0, 5) and (4, 17). Calculate the slope of the line that passes through (0, 5) and (4, 17). STEP 1 x 2 – x 1 4 – 0 y 2 – y 1 = m = 17 – 5 = 4 12 = 3 STEP 2 y = mx + b Write slope-intercept form. y = 3x + 5 Substitute 3 for m and 5 for b. Write an equation of the line. The line crosses the y -axis at (0, 5). So, the y- intercept is 5. The function is f(x) = 3x + 5.

Parallel Lines two lines in the same plane are parallel if they never intersect. Because slope gives the rate at which a line rises or falls, two lines with the SAME SLOPE are PARALLEL. y = 3x + 2 y = 3x – 4

Write an equation of the line that passes through (0, -5) and is parallel to the line y = 3x + 1. STEP 1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line will have the same slope and go through (0, -5). STEP 2 y = mx + b Write slope-intercept form. Substitute 3 for m and -5 for b. Write an equation. Use y = mx + b. y = 3x - 5

Write an equation of the line that passes through (0, 11) and is parallel to the line y = -x + 5. STEP 1 Identify the slope. The graph of the given equation has a slope of -1. So, the parallel line will have the same slope and go through (0, 11). STEP 2 y = mx + b Write slope-intercept form. Substitute -1 for m and 11 for b. Write an equation. Use y = mx + b. y = -1x + 11

Perpendicular Lines two lines in the same plane are perpendicular if they intersect at right angles. Because slope gives the rate at which a line rises or falls, two lines with slopes that are NEGATIVE RECIPROCALS are PERPENDICULAR. y = -2x + 2 y = 1/2x – 4 ½ and -2 are negative reciprocals. 4/3 and -3/4 are negative reciprocals.

Write an equation of the line that passes through (0, – 5) and is perpendicular to the line y = 2x + 3. STEP 1 Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line is -1/2. STEP 2 The graph of the given equation has a slope of -1/2. and will go through the point (0, -5). STEP 3 y = mx + b Write slope-intercept form. Substitute -1/2 for m and -5 for b. Write an equation. Use y = mx + b. y = -1/2x - 5

Homework Text p. 422, #8-22 evens, #15 & #21 Text p. 422, #8-22 evens, #15 & #21