Question

Find the equation of a line that contains the point (7,5) and has a slope of m=4/7

Answer 1

Concept: Equation of a Line

The equation of a line given a point(x,y) and the slope, m(gradient) is given by

`\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}`

given the following parameters

`x_1=7,y_1=5,m=(4)/(7)`

we then substitute into the formula above

`\begin{gathered} y-5=(4)/(7)(x-7) \\ 7(y-5)=4(x-7) \end{gathered}`

Then simplify the expression by multiplying the terns in the parenthesis

`\begin{gathered} 7y-35=4x-28 \\ 7y-4x-35+28=0 \\ 7y-4x-7=0 \\ or \\ y=(4)/(7)x+1 \end{gathered}`

Therefore the equation of the line becomes 7y-4x-7=0