Question

Find the equation for the line (2,4) and (-6,-6)

Answer 1

Given:

The given line passes through (2,4) and (-6,-6)

Required: The equation of the line

Step-by-step explanation:

First, find the slope using the two point formula.

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ =(-6-4)/(-6-2) \\ =(-10)/(-8) \\ =(5)/(4) \end{gathered}`

The slope-intercept form of a line is of the form y = mx+c, where m is the slope and c is the y-intercept.

Substitute the obtained value of m into y = mx+c.

`y=(5)/(4)x+c`

Plug the point (2, 4) into the equation to find c.

`\begin{gathered} 4=(5)/(4)\cdot2+c \\ c=4-(5)/(2) \\ =(3)/(2) \end{gathered}`

Substitute the value of c into y = (5/4)x+c.

`y=(5)/(4)x+(3)/(2)`

Final Answer:

`y=(5)/(4)x+(3)/(2)`