Question

Write the equation, in slope- intercept form, for the line shownA) y = - 4/5x - 3B) y = - 4/5x + 3C) y = - 5/4x - 3D) y = - 5/4x + 3

Answer 1

The equation of a line in slope-intercept form looks like this:

`y=mx+b`

Where m is the slope and b is the y-intercept. Any point that is part of this line must be a solution wo this equation. Looking at the picture you can see that the line passes through points (-5,1) and (0,-3). Then if we replace x and y in the former equation with the first and second coordinate of each of these points we'll have two equations:

`\begin{gathered} 1=-5m+b \\ -3=m\cdot0+b \end{gathered}`

By solving these equations we find m and b which means that we'll find the equation requested. First is important to note that the second equation tells us the value of b:

`-3=b`

If we substitute this value in the first equation we get:

`1=-5m-3`

Now let's add 3 to both sides of this equation:

`\begin{gathered} 1+3=-5m-3+3 \\ 4=-5m \end{gathered}`

And we divide both sides by -5:

`\begin{gathered} -(4)/(5)=-(5m)/(-5) \\ m=-(4)/(5) \end{gathered}`

Now that we have both m and b we have the equation in slope-intercept form:

`y=-(4)/(5)x-3`

Which means that the answer is option A.