Question

A line goes through the points (4, 5) and (2, -6). Write the equation of the line in slope- intercept form. Did I get the correct answer? Y= 11/2x - 17

Answer 1

Given:

A line passing through the points (4,5) and (2,-6).

The objective is to find the equation of line in slope-intercept form.

Step-by-step explanation:

Consider the given points as

`\begin{gathered} (x_1,y_1)=(4,5) \\ (x_2,y_2)=(2,-6) \end{gathered}`

The slope of the line can be calculated as,

`m=(y_2-y_1)/(x_2-x_1)\text{ . . . . . . .(1)}`

To find slope m:

On plugging the gven vales in rquation of slope,

`\begin{gathered} m=(-6-5)/(2-4) \\ m=(-11)/(-2) \\ m=(11)/(2) \end{gathered}`

The general equation of straight line is,

`y-y_1=m(x-x_1).......(2)_{}`

To find equation:

On plugging the values in the above equation.

`\begin{gathered} y-5=(11)/(2)(x-4) \\ y-5=(11)/(2)x-4((11)/(2)) \\ y=(11)/(2)x-22+5 \\ y=(11)/(2)x-17 \end{gathered}`

Hence, the equation of straight linne is y = (11/2)x - 17.

So the answer is correct.