Question

Find the equation of each line(b) through (5, 6) and (2, -1) (c) through (2, -1) and (-25, 26)

Answer 1

We are asked to find the equation of a line that passes through the points (5,6) and (2,-1). To do that let's remember the general equation of a line:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept. To determine the slope we will use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where:

`\begin{gathered} (x_1,y_1)=(5,6)_{} \\ (x_2,y_2)=(2,-1) \end{gathered}`

Replacing the values we get:

`m=(-1-6)/(2-5)=-(7)/(-3)=(7)/(3)`

The slope is 7/3. Replacing that value in the general equation for the line:

`y=(7)/(3)x+b`

Now we replace one of the points to get the value of "b". we will replace (x,y)=(2,-1). This means that when x = 2, y = -1.

`-1=(7)/(3)(2)+b`

Solving the operations:

`-1=(14)/(3)+b`

Now we subtract 14/3 to both sides:

`-1-(14)/(3)=b`

Solving the operations we get:

`-(17)/(3)=b`

Replacing in the equation for the line:

`y=(7)/(3)x-(17)/(3)`