11.03.2022

What are the x- and y-intercepts of the function 3x - 4y = -3?
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Mathematics

Which function has the same y-intercept as the function y=2 /3x-3? a 2/3 x + 3y = -3 b -2/3 x + 3y = 6 c x + 4y = 12 d 6x - 7y = 21 pleaz answer im in a hurry

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The equation of the function that has the same y-intercept as $y = \frac{2}{3}x - 3$ is $\mathbf{6x - 7y = 21}$ . Both functions have the y-intercept of -3.

Recall:

Equation of a line in slope-intercept form is represented as: y = mx + b

y-intercept = b

m = slope

Given the function, $y = \frac{2}{3}x - 3$ ,

the y-intercept is -3

Rewrite each given option in the slope-intercept form to find which of the function has the same y-intercept value of -3 as in the function $y = \frac{2}{3}x - 3$ .

Option A: $\frac{2}{3} x + 3y = -3$

Rewrite as y = mx + b

$\frac{2}{3} x + 3y - \frac{2}{3} x = -\frac{2}{3} x -3\\\\3y = -\frac{2}{3} x -3\\\\3y \times \frac{1}{3} = -\frac{2}{3} x \times \frac{1}{3} -3 \times \frac{1}{3}\\\\\mathbf{y = -\frac{2}{9}x - 1}$

Thus, the y-intercept is -1

Option B: $-\frac{2}{3} x + 3y = 6$

Rewrite as y = mx + b

$-\frac{2}{3} x + 3y + \frac{2}{3} x = \frac{2}{3} x + 6\\\\3y = \frac{2}{3} x + 6\\\\3y \times \frac{1}{3} = \frac{2}{3} x \times \frac{1}{3} + 6 \times \frac{1}{3}\\\\\mathbf{y = \frac{2}{9}x + 2}$

Thus, the y-intercept is 2

Option C: x + 4y = 12

Rewrite as y = mx + b

$x + 4y - x= - x + 12\\\\4y = -x + 12\\\\4y \times \frac{1}{4} = -x \times \frac{1}{4} + 12 \times \frac{1}{4} \\\\\mathbf{y = -\frac{1}{4} x + 3}$

Thus, the y-intercept is 3

Option D: 6x - 7y = 21

Rewrite as y = mx + b

$- 7y = -6x + 21 \\\\-7y \times -\frac{1}{7} = -6x \times -\frac{1}{7} + 21 \times -\frac{1}{7}\\\\\mathbf{y = \frac{6}{7}x - 3}$

Thus, the y-intercept is -3

Therefore, the equation of the function that has the same y-intercept as $y = \frac{2}{3}x - 3$ is $\mathbf{6x - 7y = 21}$ . Both functions have the y-intercept of -3.

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Mathematics

Which function has the same y-intercept as the function y=2 /3x-3? a 2/3 x + 3y = -3 b -2/3 x + 3y = 6 c x + 4y = 12 d 6x - 7y = 21 pleaz answer im in a hurry

Step-by-step answer

P Answered by PhD

The equation of the function that has the same y-intercept as $y = \frac{2}{3}x - 3$ is $\mathbf{6x - 7y = 21}$ . Both functions have the y-intercept of -3.

Recall:

Equation of a line in slope-intercept form is represented as: y = mx + b

y-intercept = b

m = slope

Given the function, $y = \frac{2}{3}x - 3$ ,

the y-intercept is -3

Rewrite each given option in the slope-intercept form to find which of the function has the same y-intercept value of -3 as in the function $y = \frac{2}{3}x - 3$ .

Option A: $\frac{2}{3} x + 3y = -3$

Rewrite as y = mx + b

$\frac{2}{3} x + 3y - \frac{2}{3} x = -\frac{2}{3} x -3\\\\3y = -\frac{2}{3} x -3\\\\3y \times \frac{1}{3} = -\frac{2}{3} x \times \frac{1}{3} -3 \times \frac{1}{3}\\\\\mathbf{y = -\frac{2}{9}x - 1}$

Thus, the y-intercept is -1

Option B: $-\frac{2}{3} x + 3y = 6$

Rewrite as y = mx + b

$-\frac{2}{3} x + 3y + \frac{2}{3} x = \frac{2}{3} x + 6\\\\3y = \frac{2}{3} x + 6\\\\3y \times \frac{1}{3} = \frac{2}{3} x \times \frac{1}{3} + 6 \times \frac{1}{3}\\\\\mathbf{y = \frac{2}{9}x + 2}$

Thus, the y-intercept is 2

Option C: x + 4y = 12

Rewrite as y = mx + b

$x + 4y - x= - x + 12\\\\4y = -x + 12\\\\4y \times \frac{1}{4} = -x \times \frac{1}{4} + 12 \times \frac{1}{4} \\\\\mathbf{y = -\frac{1}{4} x + 3}$

Thus, the y-intercept is 3

Option D: 6x - 7y = 21

Rewrite as y = mx + b

$- 7y = -6x + 21 \\\\-7y \times -\frac{1}{7} = -6x \times -\frac{1}{7} + 21 \times -\frac{1}{7}\\\\\mathbf{y = \frac{6}{7}x - 3}$

Thus, the y-intercept is -3

Therefore, the equation of the function that has the same y-intercept as $y = \frac{2}{3}x - 3$ is $\mathbf{6x - 7y = 21}$ . Both functions have the y-intercept of -3.

Learn more here:

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Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

Deanna gets 3 problems incorrect on a math quiz. Her score is 85%. How many questions are on the quiz?

Step-by-step answer

P Answered by PhD