Chapter 2 Review Equations of Lines

1. Give the domain and range:{(3,2) (5,1) (-4,2) (-3,0) (3,5)}

Is it a function?

D: {-4, -3, 3, 5}R: {0,1,2,5}

NO – 3 goes to 2 and 5.

2. Write the equation of the line with slope -3 and y-intercept 4. Graph the line. y=-3x+4

Slope-intercept: y = mx + b

y= -3x+4

3. Write the equation of the line that passes through (5,-2) and has slope of ⅔.Formula: y-y1 = m(x-x1)

y+2 = ⅔(x-5) y+2 = ⅔x-3⅓

distributeSubtract 2

y = ⅔x-5⅓

Point slope: y – y1 = m( x – x1)

4. Write the equation of the line that passes through (-1,4) and (-2,9)

Formula: y-y1 = m(x-x1)

y-4= -5(x+1) distributey-4=-5x-5 add 4y = -5x-1

m = 9-4 -2+1 = -5

Point slope: y – y1 = m( x – x1)

5. Write the equation of the line parallel to y = 2x – 7 and passes (3,-2)

Formula: y-y1 = m(x-x1)

y+2= 2(x-3) distributey+2=2x-6 Subrtact 2y = 2x-8

Point slope: y – y1 = m( x – x1)

m= 2

6. Write the equation of the line perpendicular to x + 4y = 8 and passes (-3,1)

Formula: y-y1 = m(x-x1)

y-1= 4(x+3) distributey-1=4x+12 Add 1y = 4x+13

4y = -x + 8

y = -¼x + 2 ┴ slope is 4

7. Write the equation of the line perpendicular to 2x – 3y = 6 and passes (2,-4) -3y = -2x + 6

y = ⅔x - 2 ┴ slope is -3/2

WRITE IN STANDARD FORM:Ax + By = C

y+4= -3/2(x-2)y + 4 = -3/2x + 3

y = -3/2x - 1 ( ) 22y= -3x – 2

3x + 2y = -2

8. Graph the line: 5x – 2y = 8-2y = -5x + 8

Slope-intercept: y = mx + b

y = 5/2x - 4y = 5/2x - 4

9. Graph the inequality: 2y > 3x - 8y> 3/2 x - 4

Piecewise function:

RS|T|3 123 2

x

xf(x)=

If x > -2If x ≤ -2

10. Graph the function: y = 3|x-4|+2Describe the shifts:narrower by 3, up 2 and right 4

SHIFTS OF GRAPHS

y = a|x| if a<1 get widery = a|x| if a>1 get narrowery = |x+h| moves left h unitsy = |x-h| moves right h unitsy = |x|+k moves up k units

y = |x|-k moves down k units

11. Graph the function: y = -2|x+1|-3

Describe the shifts:Reflects across the x axisnarrower by 2, down 3 and left 1.

SHIFTS OF GRAPHS

y = a|x| if a<1 get widery = a|x| if a>1 get narrowery = |x+h| moves left h unitsy = |x-h| moves right h unitsy = |x|+k moves up k units

y = |x|-k moves down k units

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