Question
Consider this system of equations. Which shows the second equation written in slope-intercept form?
[tex]y = 3x - 2.[/tex]
[tex]10(x + \frac{3}{5} ) = 2y[/tex]
A. [tex]y = 5x + \frac{3}{10}[/tex]
B. [tex]y = 5x + 3[/tex]
C. [tex]y = \frac{1}{5} x + \frac{3}{25}[/tex]
D. [tex]y = \frac{1}{2} x + 6[/tex]
Answer:
B. [tex]y = 5x + 3[/tex]
Step-by-step explanation:
Given
Equation 1: [tex]y = 3x - 2.[/tex]
Equation 2: [tex]10(x + \frac{3}{5} ) = 2y[/tex]
Required:
Equivalent of equation 2
To get an equivalent of equation 2 (in slope intercept form), first we have to simplify equation 2
[tex]10(x + \frac{3}{5} ) = 2y[/tex]
Open the bracket
[tex]10*x + 10 *\frac{3}{5} = 2y[/tex]
[tex]10x + \frac{30}{5} = 2y[/tex]
Simplify fraction
[tex]10x + 6 = 2y[/tex]
Divide through by 2
[tex]\frac{10x}{2} + \frac{6}{2} = \frac{2y}{2}[/tex]
[tex]5x + 3 = y[/tex]
Re-arrange
[tex]y = 5x + 3[/tex]
The next step is to compare each of option A through D with [tex]y = 5x + 3[/tex]
A.
[tex]y = 5x + \frac{3}{10}[/tex] is not equal to [tex]y = 5x + 3[/tex]
We check the next available option
B.
[tex]y = 5x + 3[/tex] is equal to [tex]y = 5x + 3[/tex]
This option is equivalent to the second equation in slope-intercept form.
We check further if there are more equivalent options
C.
[tex]y = \frac{1}{5} x + \frac{3}{25}[/tex]
Convert fraction to decimal
[tex]y = 0.2x + 0.12[/tex]
This is not equal to [tex]y = 5x + 3[/tex]
D.
[tex]y = \frac{1}{2} x + 6[/tex]
Convert fraction to decimal
[tex]y = 0.5x + 6[/tex]
This is not equal to [tex]y = 5x + 3[/tex]
Hence, the only equation that is equivalent to the second equation written in slope intercept form is Option B
Answer:
The answer is B
Step-by-step explanation:
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