Solution
Given the equation
[tex]y=-\frac{5}{4}x+\frac{11}{4}[/tex]
Here, the radient is;
[tex]m=-\frac{5}{4}[/tex]
Since the line in question is perpendicular to the given line,
The product of their gradient mst be -1
[tex]\begin{gathered} m_1\times m=-1 \\ \\ \Rightarrow m_1=-\frac{1}{m} \\ \\ \text{ since }m=-\frac{5}{4} \\ \\ \Rightarrow m_1=-\frac{1}{-\frac{5}{4}}=\frac{4}{5} \end{gathered}[/tex]
Therefore, the gradient of the line in questin is 4/5
Since the line passes trough the poinyt (0, 7)
[tex]\begin{gathered} \Rightarrow\frac{y_-y_1}{x-x_1}=m \\ \\ \Rightarrow\frac{y-7}{x-0}=\frac{4}{5} \\ \\ \Rightarrow\frac{y-7}{x}=\frac{4}{5} \\ \\ \Rightarrow y-7=\frac{4}{5}x \\ \\ \Rightarrow y=\frac{4}{5}x+7 \end{gathered}[/tex]
Hence, the correct option is A.
