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Math  /  Algebra

Question7. Match each equation with the slope mm and yy-intercept of its graph (y=mx+b)(\mathrm{y}=\mathrm{mx}+\mathrm{b}) A. m=−6,y−m=-6, y- int =(0,12)=(0,12)
1. 5x−6y=305 x-6 y=30 B. m=−6,y−int=(0,5)m=-6, y-i n t=(0,5)
2. y=5−6xy=5-6 x C. m=−56,y−m=-\frac{5}{6}, y- int =(0,1)=(0,1)
3. y=56x+1y=\frac{5}{6} x+1 D. m=56,y−m=\frac{5}{6}, y- int =(0,1)=(0,1)
4. 5x−6y=65 x-6 y=6 E. m=56,y−\quad m=\frac{5}{6}, y- int =(0,−1)=(0,-1)
5. 5x+6y=65 x+6 y=6
6. 6x+y=126 x+y=12 F. m=56,y−int=(0,−5)\quad m=\frac{5}{6}, y-i n t=(0,-5)

Studdy Solution

STEP 1

1. Each equation is in the form of a linear equation that can be rewritten in the slope-intercept form y=mx+b y = mx + b .
2. We need to match each equation with the given slope m m and y y -intercept b b .

STEP 2

1. Convert each equation to the slope-intercept form y=mx+b y = mx + b .
2. Identify the slope m m and y y -intercept b b for each equation.
3. Match each equation with the corresponding slope and y y -intercept.

STEP 3

Convert the equation 5x−6y=30 5x - 6y = 30 to slope-intercept form: 5x−6y=30 5x - 6y = 30 −6y=−5x+30 -6y = -5x + 30 y=56x−5 y = \frac{5}{6}x - 5

STEP 4

Identify the slope and y y -intercept for y=56x−5 y = \frac{5}{6}x - 5 : - Slope m=56 m = \frac{5}{6} - y y -intercept = (0,−5) (0, -5)

STEP 5

Match the equation 5x−6y=30 5x - 6y = 30 with the given options: - Matches with F: m=56,y-int=(0,−5) m = \frac{5}{6}, y\text{-int} = (0, -5)

STEP 6

Convert the equation y=5−6x y = 5 - 6x to slope-intercept form: y=−6x+5 y = -6x + 5

STEP 7

Identify the slope and y y -intercept for y=−6x+5 y = -6x + 5 : - Slope m=−6 m = -6 - y y -intercept = (0,5) (0, 5)

STEP 8

Match the equation y=5−6x y = 5 - 6x with the given options: - Matches with B: m=−6,y-int=(0,5) m = -6, y\text{-int} = (0, 5)

STEP 9

Convert the equation y=56x+1 y = \frac{5}{6}x + 1 to slope-intercept form: y=56x+1 y = \frac{5}{6}x + 1

STEP 10

Identify the slope and y y -intercept for y=56x+1 y = \frac{5}{6}x + 1 : - Slope m=56 m = \frac{5}{6} - y y -intercept = (0,1) (0, 1)

STEP 11

Match the equation y=56x+1 y = \frac{5}{6}x + 1 with the given options: - Matches with D: m=56,y-int=(0,1) m = \frac{5}{6}, y\text{-int} = (0, 1)

STEP 12

Convert the equation 5x−6y=6 5x - 6y = 6 to slope-intercept form: 5x−6y=6 5x - 6y = 6 −6y=−5x+6 -6y = -5x + 6 y=56x−1 y = \frac{5}{6}x - 1

STEP 13

Identify the slope and y y -intercept for y=56x−1 y = \frac{5}{6}x - 1 : - Slope m=56 m = \frac{5}{6} - y y -intercept = (0,−1) (0, -1)

STEP 14

Match the equation 5x−6y=6 5x - 6y = 6 with the given options: - Matches with E: m=56,y-int=(0,−1) m = \frac{5}{6}, y\text{-int} = (0, -1)

STEP 15

Convert the equation 5x+6y=6 5x + 6y = 6 to slope-intercept form: 5x+6y=6 5x + 6y = 6 6y=−5x+6 6y = -5x + 6 y=−56x+1 y = -\frac{5}{6}x + 1

STEP 16

Identify the slope and y y -intercept for y=−56x+1 y = -\frac{5}{6}x + 1 : - Slope m=−56 m = -\frac{5}{6} - y y -intercept = (0,1) (0, 1)

STEP 17

Match the equation 5x+6y=6 5x + 6y = 6 with the given options: - Matches with C: m=−56,y-int=(0,1) m = -\frac{5}{6}, y\text{-int} = (0, 1)

STEP 18

Convert the equation 6x+y=12 6x + y = 12 to slope-intercept form: 6x+y=12 6x + y = 12 y=−6x+12 y = -6x + 12

STEP 19

Identify the slope and y y -intercept for y=−6x+12 y = -6x + 12 : - Slope m=−6 m = -6 - y y -intercept = (0,12) (0, 12)

STEP 20

Match the equation 6x+y=12 6x + y = 12 with the given options: - Matches with A: m=−6,y-int=(0,12) m = -6, y\text{-int} = (0, 12)
The matches are:
1. 5x−6y=30 5x - 6y = 30 matches with F.
2. y=5−6x y = 5 - 6x matches with B.
3. y=56x+1 y = \frac{5}{6}x + 1 matches with D.
4. 5x−6y=6 5x - 6y = 6 matches with E.
5. 5x+6y=6 5x + 6y = 6 matches with C.
6. 6x+y=12 6x + y = 12 matches with A.

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