Precalculus Quiz 2

Slope intercept form

y=mx+b

Write the equation of each line with the given information:

m= 2

b= 5

y= 2x+5

Write the equation of each line with the given information:

m= -3

b= 2

y= x-3+2

Write the equation of each line with the given information:

m= \frac23

b= -\frac35

y= \frac23 x - \frac35

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(2,7) ; m= -4

y - 7 = -4(x - 2)

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(12,5) ; m= -3

y - 5 = -3(x - 12)

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(4, -5) ; (9,6)

To write the Point Slope Form of two points you can choose either point as the y1 and x1. to find the slope (m) = \frac{y2-y1}{x2-x1} for this problem: \frac{6-\left(-5\right)}{9-4} so 6+5=11 and 9-4=5 and that is how we get \frac{11}{5}

y - (-5) = \frac{11}{5} (x - 4)

y+5 = \frac{11}{5} (x - 4)

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(-6, -2) ; m= 3

y - (-2) = 3 (x- (-6))

y+2= 3(x+6)

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(7, -6) ; m= \frac12

y - (-6) = \frac12 (x -7)

y+6 = \frac12 (x -7)

to make it without the fraction multiply the 2 in the denominator to the other side:

2( y+6) = 1 (x - 7)

2y+12= x - 7

Point Slope Form: y - y1 = m (x - x1)

Write the equation of each line in Point - Slope Form:

(-8,2) ; m= -\frac34

y - 2 = -\frac34 (x- (-8))

y - 2 = -\frac34 (x-+8)

Standard Form: Ax + By = C

Write each equation in Standard Form with the given information then identify the values of A, B, C

Slope = \frac35 , y-intercept = 5

1. Slope intercept form = mx+b

   m = \frac35

   b = 5

   y =\frac35x + 5

2. Get rid of the fraction (m) by multiplying denominator to the other side

   y =\frac35x +

   (5)y =\frac35 x + 5 (5)

   5y = 3x + 25

   -3x -3x

   ————--

   -3x + 5y = 25

3. A = -3

   B = 5

   C = 25

Standard Form: Ax + By = C

Write each equation in Standard Form with the given information then identify the values of A, B, C

Slope = 1, y-intercept = -3

1. Slope intercept form = mx+b

   m = 1

   b = -3

   y = 1x - 3

2. Get x to the other side to be with y.

   y = 1x - 3

   -1x -1x

   ————--

   -1x + y = -3

3. A = -1

   B = 1

   C = -3

Standard Form: Ax + By = C

Write each equation in Standard Form with the given information then identify the values of A, B, C

Slope = - \frac35 , y-intercept = -3

1. Slope intercept form = mx+b

   m = - \frac35

   b = -3

   y = -\frac35x - 3

2. Get rid of the fraction (m) by multiplying denominator to the other side

   y = -\frac35x - 3

   (5)y = -\frac35 x - 3 (5)

   5y = -3x - 15

   +3x +3x

   ————--

   3x + 5y = -15

3. A = 3

   B = 5

   C = -15

Standard Form: Ax + By = C

Write each equation in Standard Form with the given information then identify the values of A, B, C

Slope = \frac54 , y-intercept = 2

1. Slope intercept form = mx+b

   m = \frac54

   b = 2

   y =\frac54 x + 2

2. Get rid of the fraction (m) by multiplying denominator to the other side

   y = \frac54 x + 2

   (4)y = \frac54 x + 2 (4)

   4y = 5x + 8

   -5x -5x

   ————--

   -5x + 4y = 8

3. A = -5

   B = 4

   C = 8

Find the slope of each line. Write each equation in Slope - Intercept Form.

3x - 2y = -16

Slope - Intercept form = y=mx + b

1. 3x - 2y = -16

2. Isolate the B so subtract 3x

   3x - 2y = -16

   -3x -3x

   ——————--

   -2y = -3x - 16

3. Divide by -2

\frac{-2y}{-2} = \frac{-3x}{-2} - \frac{-16}{-2}

y = \frac32x - 8

m = \frac32

Find the slope of each line. Write each equation in Slope - Intercept Form.

13x - 11y = -12

Slope - Intercept form = y=mx + b

1. 13x - 11y = -12

2. Isolate the B so subtract 13x

   13x - 11y = -12

   -13x -13x

   ——————--

   -11y = -13x - 12

3. Divide by -11

\frac{-11y}{-11} = \frac{-13x}{-11} - \frac{-12}{-11}

y = \frac{13}{11}x + \frac{12}{11}

m = \frac{13}{11}

Find the slope of each line. Write each equation in Slope - Intercept Form.

9x - 7y = -7

Slope - Intercept form = y=mx + b

1. 9x - 7y = -7

2. Isolate the B so subtract 9x

   9x - 7y = -7

   -9x -9x

   ——————--

   -7y = -9x - 7

3. Divide by -7

\frac{-7y}{-7} = \frac{-9x}{-7} \frac{-7}{-7}

y = \frac{9x}{7} x + 1

m = \frac97

Find the slope of each line. Write each equation in Slope - Intercept Form.

x - 3y = 6

Slope - Intercept form = y=mx + b

1. x - 3y = 6

2. Isolate the B so subtract x

   x - 3y = 6

   -x -x

   ——————--

   -3y = -x + 6

3. Divide by -3

\frac{-3y}{-3} = \frac{-x}{-3} \frac{6}{-3}

y = \frac13x - 2

m = \frac13

Find the slope of each line. Write each equation in Slope - Intercept Form.

6x + 5y = -15

Slope - Intercept form = y=mx + b

1. 6x + 5y = -15

2. Isolate the B so subtract 6x

   6x + 5y = -15

   -6x -6x

   ——————--

   5y = -6x - 15

3. Divide by 5

\frac{5y}{5} = \frac{-6x}{5} \frac{-15}{5}

y = \frac{-6}{5} x - 3

m = \frac{-6}{5}

Find the slope of each line. Write each equation in Slope - Intercept Form.

4x - y = 1

Slope - Intercept form = y=mx + b

1. 4x - y = 1

2. Isolate the B so subtract 4x

   4x - y = 1

   -4x -4x

   ——————--

   -y = -4x + 1

3. Divide by -1

\frac{-y}{-1} = \frac{-4x}{-1} \frac{1}{-1}

y = 4x - 1

m = 4

Graph the equation below:

y+4 = -3(x+2)

m = -3

(-2,-4)

Graph the equation below:

y+3 = -2(x-2)

m = -2

(2, -3)

Graph the equation below:

y-1 = 3(x+6)

m = 3

(-6, 1)

Graph the equation below:

y+4 = \frac{-5}{2}(x-3)

m = \frac{-5}{2}

(3, -4)

With the given information, write the equation of each line in slope-intercept or point-slope form then write it in standard form.

m = -5 ; b = 3

slope int = y = -5x + 3

standard form = 5x + y = 3

point slope form = y + 2 = -5 (x-1)

With the given information, write the equation of each line in slope-intercept or point-slope form then write it in standard form.

(1,2) ; slope = 7

slope int = y = 7x - 5

standard form = 7x - y = 5

point slope form = y - 2 = 7 (x - 1)

With the given information, write the equation of each line in slope-intercept or point-slope form then write it in standard form.

Passing through the point (3,5) , slope = \frac53

point slope form = y - 5 = \frac53 ( x - 3 )

slope int = y - 5 = \frac53 ( x - 3 )

y - 5 = \frac53x - \frac53 (3)

y - 5 = \frac53 x - 5

+5 +5

———————-

y = \frac53 x

slope int: y =\frac53 \frac53 x

standard form =

Ax + By = C

Slope int : y = \frac53 x

(3) y = \frac53 x (3)

3y = 5x

-5x -5x

————-

-5x + 3y = 0

(To make A positive) you can multiply A and B by -1

(-1) -5x + (-1) 3y = 0

5x - 3y = 0

Standard Form:

-5x + 3y = 0

OR

5x - 3y = 0

With the given information, write the equation of each line in slope-intercept or point-slope form then write it in standard form.

Connecting the points (1,5) ; (3,4)

point slope form: y - 5 = -\frac12 (x - 1)

standard form:

y - 5 =-\frac12 (x -1)

2(y - 5) = (2)-\frac12 (x-1)

2y - 10 = -1 (x - 1)

2y - 10 = -1x + 1

+10 +10

—————————

2y = -1x +11

-1x -1x

——————-

-1x + 2y = 11

→ x + 2y = 11

Identify the values of A, B , and C, then find the slope of each equation:

5x + 10y = 15

A = 5

B = 10

C = 15

m = \frac{-A}{B}

m = \frac{-5}{10}

Identify the values of A, B , and C, then find the slope of each equation:

-3x + 2y = 12

A = -3

B = 2

C = 12

m = \frac{-A}{B}

m = \frac32

Identify the values of A, B , and C, then find the slope of each equation:

7x - 21y = 10

A = 7

B = -21

C = 10

m = \frac{-A}{B}

m = \frac{-7}{-21} OR → m = \frac{7}{21}