Question

Point Slope FormulaWrite the equation of a line given two points.(1.4) and (6.-1)First find the slope between the two lines and enter that answer below. Remember to simplify your fractions.M=____Then, use your slope to find the equation of the line.Y=___x+___

Answer 1

y=-x+5

Step-by-step explanation

Step 1

if you have two points of a line P1 and P2, the slope is given by:

`\begin{gathered} \text{slope}=\text{ }(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1)\text{ and }P2(x_2,y_2) \end{gathered}`

Let

P1=(1,4)

P2=(6,-1)

replace,

`\begin{gathered} \text{slope}=\text{ }(y_2-y_1)/(x_2-x_1) \\ \text{slope}=\text{ }(-1-4)/(6-1)=(-5)/(5)=-1 \\ \text{slope}=-1 \end{gathered}`

Step 2

find the Point -slope equation using the slope founded and P1

`\begin{gathered} y-y_1=slope(x-x_1) \\ \text{replace} \\ y-4=-1(x-1) \\ y-4=-x+1 \\ y=-x+1+4 \\ y=-x+5 \end{gathered}`

I hope this helps you.