Do Now 6/10/10Do Now 6/10/10Take out HW from last night.Take out HW from last night.

–Text p. 411, #1-10 allText p. 411, #1-10 all

Copy HW in your planner. Copy HW in your planner. –Text p. 422, #8-22 even, #15 & #21Text p. 422, #8-22 even, #15 & #21

In your notebook, answer the following question. In your notebook, answer the following question. Can you write an equation for the line on the Can you write an equation for the line on the graph?graph?

HomeworkHomework Text p. 411, #1-10 all Text p. 411, #1-10 all

1) parallel1) parallel 2) perpendicular2) perpendicular 3) perpendicular3) perpendicular 4) parallel4) parallel 5) no; they lie in 5) no; they lie in

the same line.the same line.

6) no; they 6) no; they intersectintersect

7) yes; they do not 7) yes; they do not lie in the same lie in the same plane and do not plane and do not intersectintersect

8) lines AG, CE, EF8) lines AG, CE, EF 9) lines BD, EG9) lines BD, EG 10) lines HJ, EG10) lines HJ, EG

ObjectiveObjective

SWBAT write linear equations SWBAT write linear equations

Section 8.6 Section 8.6 “Writing Linear Equations”“Writing Linear Equations”

SLOPE-INTERCEPT FORM-SLOPE-INTERCEPT FORM-a linear equation written in the a linear equation written in the formform

y = mx + by = mx + bslope y-intercepty-coordinate x-coordinate

You can write a linear equation in You can write a linear equation in slope-intercept form, if you know the slope slope-intercept form, if you know the slope ((m)m) and the y-intercept ( and the y-intercept (b)b) of the of the equation’s graph.equation’s graph.

Slope ReviewSlope Review

The slope The slope m m of a line passing through two pointsof a line passing through two points

and is the ratio of the rise and is the ratio of the rise change to the run. change to the run.

),( 11 yx ),( 22 yx

m

y

x

),( 11 yx

),( 22 yx

runrun

riserise)( 12 yy

)( 12 xx

The graph crosses The graph crosses the the yy--axis at axis at (0, 2).(0, 2). The The y-y-intercept isintercept is 2. 2.

Write an equation of the line shown.Write an equation of the line shown.

y = mx + by = mx + b

The slope of the line The slope of the line is ais a rise of 2rise of 2 and aand a run of 4.run of 4. The slope is The slope is 1/21/2..

y = ½x + 2y = ½x + 2

The graph crosses The graph crosses the the yy--axis at axis at (0, -1).(0, -1). The The y-y-intercept isintercept is -1. -1.

Write an equation of the line shown.Write an equation of the line shown.

y = mx + by = mx + b

The slope of the line The slope of the line is ais a rise of 1rise of 1 and aand a run of 2.run of 2. The slope is The slope is 1/21/2..

y = ½x – 1y = ½x – 1

y = mx + b

y = x – 543

Substitute for m and 5 for b.43

–

STEP 1

Write an equation of the line. The line crosses the y-axis at (0, – 5). So, the y-intercept is – 5.

x2 – x1 33 – 0y2 – y1=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).

x2 – x1 -6 – 0y2 – y1=m =

0 – (-24)= -6

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

x2 – x1 4 – 0y2 – y1=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 LinesParallel Linestwo lines in the same plane are two lines in the same plane are

parallel if they never intersect. Because parallel if they never intersect. Because slope gives the rate at which a line rises or slope gives the rate at which a line rises or falls, two lines with the falls, two lines with the SAME SLOPESAME SLOPE are are PARALLELPARALLEL..

y = y = 33x + 2x + 2

y = y = 33x – 4 x – 4

Write an equation of the line that passes through Write an equation of the line that passes through (0, -5)(0, -5) and is parallel to the lineand is parallel to the line yy = 3= 3xx + 1 + 1..

STEP 1Identify 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

yy = = mxmx + + bb Write slope-intercept formWrite slope-intercept form..

SubstituteSubstitute 3 3 forfor m m andand -5 -5 forfor bb..

Write an equation. Use y = mx + b.

y = 3x - 5

Write an equation of the line that passes through Write an equation of the line that passes through (0, 11)(0, 11) and is parallel to the lineand is parallel to the line yy = -= -xx + 5 + 5..

STEP 1Identify 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

yy = = mxmx + + bb Write slope-intercept formWrite slope-intercept form..

SubstituteSubstitute -1 -1 forfor m m andand 11 11 forfor bb..

Write an equation. Use y = mx + b.

y = -1x + 11

Perpendicular Perpendicular LinesLines

two lines in the same plane are two lines in the same plane are perpendicular if they intersect at right angles. perpendicular if they intersect at right angles. Because slope gives the rate at which a line Because slope gives the rate at which a line rises or falls, two lines with slopes that are rises or falls, two lines with slopes that are NEGATIVE RECIPROCALSNEGATIVE RECIPROCALS are are PERPENDICULARPERPENDICULAR..

y = y = -2-2x + 2x + 2

y = y = 1/21/2x – 4 x – 4

½ and -2 are ½ and -2 are negative reciprocals.negative reciprocals.

4/3 and -3/4 4/3 and -3/4 are negative reciprocals.are negative reciprocals.

Write an equation of the line that passes through Write an equation of the line that passes through (0, – 5(0, – 5) and is perpendicular to the line ) and is perpendicular to the line y y = 2= 2xx + 3.+ 3.

STEPSTEP 11Identify the slope. The graph of the given equation has a slope of Identify the slope. The graph of the given equation has a slope of 22. . Because the slopes of perpendicular lines are negative reciprocals, the Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line is -1/2slope of the perpendicular line is -1/2..

STEP 2The graph of the given equation has a slope of -1/2. and will go through the point (0, -5).

STEP 3

yy = = mxmx + + bb Write slope-intercept form.Write slope-intercept form.

SubstituteSubstitute -1/2 -1/2 forfor m m andand -5 -5 forfor bb..

Write an equation. Use y = mx + b.

y = -1/2x - 5

HomeworkHomework

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