Answer :
Answer:
D. y=2/3x+7
Step-by-step explanation:
Took the test, Got it right.
The equation of line which is parallel to [tex]y=\frac{2}{3}x - 5[/tex] and passing through the point (6, 11) is [tex]y = \frac{2}{3} x+7[/tex].
What is the formula for equation of line passing through a point [tex](x_{1} ,y_{1} )[/tex]and whose slope is m?
The equation of line which is passing through [tex](x_{1},y_{1} )[/tex] and whose slope is m is given by
[tex](y - y_{1} ) = m(x-x_{1} )[/tex]
According to the given question.
We have a equation of line
[tex]y = \frac{2}{3}x-5...(i)[/tex]
And a point (6, 11).
Now, the slope of the equation of line (i)
Since, the given equation is already in slope intercept form.
So, the slope of line (i) is [tex]\frac{2}{3}[/tex]
Therefore, the equation of line which is parallel to the line (i) and passing through the point (6, 11) is given by
[tex](y - 11) = \frac{2}{3} (x - 6)[/tex] ( slope of parallel lines are equals)
⇒[tex]y -11 = \frac{2}{3}x - 4[/tex]
⇒[tex]y = \frac{2}{3}x - 4 +11[/tex]
⇒ [tex]y = \frac{2}{3} x+7[/tex]
Hence, the equation of line which is parallel to [tex]y=\frac{2}{3}x - 5[/tex] and passing through the point (6, 11) is [tex]y = \frac{2}{3} x+7[/tex].
Thus, option D is correct.
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