Question

Find the equation of given points. Write the equation in slope-intercept form. (2,5)(6,1)

Answer 1

Equation of a line in slope-intercept form

`y=mx+b`

where m is the slope and b is the y-intercept.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

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

This line passes through (2,5) and (6,1), then its slope is:

`m=(1-5)/(6-2)=(-4)/(4)=-1`

Substituting with the point (2, 5) and m = -1 into the general equation and solving for b:

`\begin{gathered} 5=\lparen-1)\cdot2+b \\ 5=-2+b \\ 5+2=b \\ 7=b \end{gathered}`

Substituting with m = -1 and b = 7 into the general equation, the equation of this line is:

`y=-x+7`