Question

Determine an equation for the line that has a slope of 4 and a solution at (-2,-13).

Answer 1

The equation of a line is given by

`\begin{gathered} y=mx+c \\ \text{where m=slope and c = intercept on y} \end{gathered}`

From the question, we have the following

`\begin{gathered} \text{slope,m}=4 \\ \text{ point(-2,-13)} \end{gathered}`

Using the slope and one point form,

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m=4,} \\ x_1=-2,y_1=-13 \end{gathered}`

Substituting the parameters into the formula, we obtain

`\begin{gathered} y-(-13)=4(x-(-2)) \\ y+13=4(x+2) \\ \end{gathered}`

The expand the parenthesis and simplify

`\begin{gathered} y+13=4x+8_{}^{} \\ y=4x+8-13 \\ y=4x-5 \end{gathered}`

Hence

The equation of the line is

y=4x-5 or y-4x=-5