Question

write the equation of the line that passes through the points (3,5) and (-2,6) Write the answer in point-slope form.

Answer 1

Let's begin by listing out the information given to us:

(x, y) = (3, 5), (-2, 6)

The general equation of a straight line function is given as:

`\begin{gathered} y=mx+b \\ where\colon m=slope,b=y-intercept \end{gathered}`

We calculate the slope using:

`\begin{gathered} m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)=(6-5)/(-2-3)=-(1)/(5) \\ m=-(1)/(5) \end{gathered}`

Substitute the slope into the, we have:

`y=-(1)/(5)x+b`

We will proceed to for b, we have:

`\begin{gathered} y=mx+b \\ m=-(1)/(5),(x,y)=(3,5) \\ 5=-(1)/(5)(3)+b\Rightarrow5=-(3)/(5)+b \\ 5=-(3)/(5)+b\Rightarrow b=5+(3)/(5) \\ b=(28)/(5) \\ y-y_1=m(x-x_1) \\ y-5=-(1)/(5)(x-3)\Rightarrow y-5=-(1)/(5)x+(3)/(5) \\ y-5=-(1)/(5)x+(3)/(5)(point-slopeform) \\ \end{gathered}`