Question

What is the equation of the line that passes through the point (-5, 2) and has aslope of 4/5?

Answer 1

To solve the exercise you can use the point-slope formula, that is,

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}`

So, in this case, you have

`\begin{gathered} m=(4)/(5) \\ (x_1,y_1)=(-5,2) \end{gathered}`
`\begin{gathered} y-y_1=m(x-x_1) \\ y-2_{}=(4)/(5)(x-(-5)) \\ y-2_{}=(4)/(5)(x+5) \\ y-2_{}=(4)/(5)x+4 \\ \text{ Add 2 from both sides of the equation} \\ y-2_{}+2=(4)/(5)x+4+2 \\ y=(4)/(5)x+6 \end{gathered}`

Therefore, the equation of the line that passes through the point (-5, 2) and has a slope of 4/5 is

`y=(4)/(5)x+6`