Question

A line passes through the point (4,7) and has slope of 5/4. Write an equation in slope intercept form for this line.

Answer 1

Given the point (4,7) and the slope 5/4, we can use the line equation in the form slope-point to get the following:

`\begin{gathered} (x_0,y_0)=(4,7) \\ m=(5)/(4) \\ y-y_0=m(x-x_0) \\ \Rightarrow y-7=(5)/(4)(x-4)=(5)/(4)x-(5\cdot4)/(4)=(5)/(4)x-5 \\ \Rightarrow y=(5)/(4)x-5+7=(5)/(4)x+2 \\ y=(5)/(4)x+2 \end{gathered}`

therefore, the equation in slope intercept form is y = 5/4x + 2