Question

What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope intercept form 1. Y=2/5x+1/52. Y=2/5x-1/53. Y= -2/5x-1/5

Answer 1

We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:

`y-y_0=m(x-x_0)`

Where:

`\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}`

Now, we plug in the values:

`y-(-1)=(2)/(5)(x-(-3))`

Simplifying we get:

`y+1=(2)/(5)(x+3)`

Now, we apply the distributive law:

`y+1=(2)/(5)x+(6)/(5)`

Now, we subtract 1 from both sides:

`\begin{gathered} y=(2)/(5)x+(6)/(5)-1 \\ \\ y=(2)/(5)x+(1)/(5) \end{gathered}`

and thus we get the equation of the line.