Question

Which of the following is the equation1) and (1, 2)?the line that passes through the points with coordinates (-2,

Answer 1

The form of the linear equation is

`y=mx+b`

m is the slope of rule

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

b is the y-intercept

Since the line passes through points (1, 2), (-2, 1), then

`\begin{gathered} x_1=-2,y_1=1 \\ x_2=1,y_2=2 \end{gathered}`

Substitute them in the rule of m to find it

`\begin{gathered} m=(2-1)/(1-(-2)) \\ m=(1)/(1+2) \\ m=(1)/(3) \end{gathered}`

Substitute it in the form of the equation

`y=(1)/(3)x+b`

To find b substitute x by 1 and y by 2 in the equation

`\begin{gathered} 2=(1)/(3)(1)+b \\ 2=(1)/(3)+b \end{gathered}`

Subtract 1/3 from both sides to find b

`\begin{gathered} 2-(1)/(3)=(1)/(3)-(1)/(3)+b \\ (6)/(3)-(1)/(3)=b \\ (5)/(3)=b \end{gathered}`

The equation of the line is

`y=(1)/(3)x+(5)/(3)`