Question

Use point-slope form to write the equation of a line that passes through the point (-1,4) with slope 5/6

Answer 1

The equation of the line is:

`6y-5x=29`

SOLUTION

Problem Statement

The question gives us a point on a line (-1, 4) and a slope of 5/6 and we are required to find the equation of the line.

Method

To find the equation of a line, we use the point-slope equation formula given below:

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where,} \\ m=\text{slope of the line} \\ (x_1,y_1)=\text{The point on the line} \end{gathered}`

Implementation

`\begin{gathered} \text{The point given to us is: }(-1,4) \\ (x_1,y_1)=(-1,4),m=(5)/(6) \\ \\ \text{Applying the point-slope formula, we have:} \\ y-4=(5)/(6)(x-(-1)) \\ y-4=(5)/(6)(x+1) \\ \text{ Multiply both sides by 6} \\ 6(y-4)=6*(5)/(6)(x+1) \\ 6(y-4)=5(x+1) \\ \\ \text{Expand the brackets, we have:} \\ 6y-6\mleft(4\mright)=5x+5(1) \\ 6y-24=5x+5 \\ \text{ Rewriting the equation, we have:} \\ 6y-5x=24+5 \\ \\ \therefore6y-5x=29 \end{gathered}`

Final Answer

The equation of the line is:

`6y-5x=29`