Question

Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)

Answer 1

`y=(2)/(5)x+(11)/(5)`

Step-by-step explanation:

Given the slope and a point on the line, we use the point-slope form to find the equation of the line:

`\begin{gathered} y-y_1=m(x-x_1) \\ m=(2)/(5) \\ (x_1,y_1)=(-3,1) \end{gathered}`

Substitute the given values:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-1=(2)/(5)(x-(-3)) \\ y-1=(2)/(5)(x+3) \\ y=(2)/(5)(x+3)+1 \\ y=(2)/(5)x+(6)/(5)+1 \\ y=(2)/(5)x+(11)/(5) \end{gathered}`

The equation of the line in slope-intercept form is:

`y=(2)/(5)x+(11)/(5)`