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Identify the equation in slope-intercept form for the line containing the point (0, 7) and perpendicular to y=-5/4x + 11/4.

Identify the equation in slope-intercept form for the line containing the point (0, 7) and-example-1
User Bnsmith
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1 Answer

2 votes

Solution

Given the equation


y=-(5)/(4)x+(11)/(4)

Here, the radient is;


m=-(5)/(4)

Since the line in question is perpendicular to the given line,

The product of their gradient mst be -1


\begin{gathered} m_1* m=-1 \\ \\ \Rightarrow m_1=-(1)/(m) \\ \\ \text{ since }m=-(5)/(4) \\ \\ \Rightarrow m_1=-(1)/(-(5)/(4))=(4)/(5) \end{gathered}

Therefore, the gradient of the line in questin is 4/5

Since the line passes trough the poinyt (0, 7)


\begin{gathered} \Rightarrow(y_-y_1)/(x-x_1)=m \\ \\ \Rightarrow(y-7)/(x-0)=(4)/(5) \\ \\ \Rightarrow(y-7)/(x)=(4)/(5) \\ \\ \Rightarrow y-7=(4)/(5)x \\ \\ \Rightarrow y=(4)/(5)x+7 \end{gathered}

Hence, the correct option is A.

User Avaynshtok
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