Question

Suppose I told you that the slope of a line was -4 and it passes through the point (1,3). How would you goabout writing the equation of that line? Do we have enough information? If not, what do we need? How can wefind it?

Answer 1

`y=-4x+7`

1) Since we know the slope is m=-4, and we have one point (1,3) then we can write out the equation of the line, plugging those pieces of information into the Point-Slope formula:

`\begin{gathered} (y-y_1)=m(x-x_1)_{} \\ y-3=-4(x-1) \\ y-3=-4x+4 \\ y-3+3=-4x+4+3 \\ y=-4x+7 \end{gathered}`

Note that ended up on the Slope-intercept form (y=mx+b).

2) So we can answer those questions as:

Plugging the data into the Point-Slope formula.

Yes, we have enough information to write out a function's rule.