Question

Find equation of a line with given slope and containing the given point. Write equation in slope-intercept form. M= 5/8, point (8,1)

Answer 1

The equation of a line in slope-intercept form is generally given as;

`y=mx+b`

Where the variables are;

`\begin{gathered} m=\text{slope} \\ b=y-\text{intercept} \\ (x,y)=(8,1) \end{gathered}`

With the slope given as 5/8, we shall substitute the known values into the equation and we'll now have;

`\begin{gathered} y=mx+b \\ 1=(5)/(8)(8)+b \\ 1=5+b \\ \text{Subtract 5 from both sides;} \\ -4=b \end{gathered}`

We now have the value of b, and the value of m (already given).

We substitute these into the general equation in slope-intercept form and we have;

`\begin{gathered} y=mx+b \\ y=(5)/(8)x+(-4) \\ y=(5)/(8)x-4 \end{gathered}`

ANSWER:

The equation of the line is;

`\begin{gathered} y=(5)/(8)x-4 \\ OR \\ y=(5x)/(8)-4 \end{gathered}`