Question

Consider this system of equations. Which shows the second equation written in slope-intercept form? y = 3 x minus 2. 10 (x + three-fifths) = 2 y y = 5 x + StartFraction 3 Over 10 EndFraction y = 5 x + 3 y = one-fifth x + StartFraction 3 Over 25 EndFraction y = one-half x + 6

Answer 1

Answer:

The answer is B

Step-by-step explanation:

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Answer 2

Question

Consider this system of equations. Which shows the second equation written in slope-intercept form?

$y = 3x - 2.$

$10(x + \frac{3}{5} ) = 2y$

A. $y = 5x + \frac{3}{10}$

B. $y = 5x + 3$

C. $y = \frac{1}{5} x + \frac{3}{25}$

D. $y = \frac{1}{2} x + 6$

Answer:

B. $y = 5x + 3$

Step-by-step explanation:

Given

Equation 1: $y = 3x - 2.$

Equation 2: $10(x + \frac{3}{5} ) = 2y$

Required:

Equivalent of equation 2

To get an equivalent of equation 2 (in slope intercept form), first we have to simplify equation 2

$10(x + \frac{3}{5} ) = 2y$

Open the bracket

$10*x + 10 *\frac{3}{5} = 2y$

$10x + \frac{30}{5} = 2y$

Simplify fraction

$10x + 6 = 2y$

Divide through by 2

$\frac{10x}{2} + \frac{6}{2} = \frac{2y}{2}$

$5x + 3 = y$

Re-arrange

$y = 5x + 3$

The next step is to compare each of option A through D with $y = 5x + 3$

A.

$y = 5x + \frac{3}{10}$ is not equal to $y = 5x + 3$

We check the next available option

B.

$y = 5x + 3$ is equal to $y = 5x + 3$

This option is equivalent to the second equation in slope-intercept form.

We check further if there are more equivalent options

C.

$y = \frac{1}{5} x + \frac{3}{25}$

Convert fraction to decimal

$y = 0.2x + 0.12$

This is not equal to $y = 5x + 3$

D.

$y = \frac{1}{2} x + 6$

Convert fraction to decimal

$y = 0.5x + 6$

This is not equal to $y = 5x + 3$

Hence, the only equation that is equivalent to the second equation written in slope intercept form is Option B