Question

Find the equation (in terms of x ) of the line through the points (-4,5) and (2,1)y=

Answer 1

Given:

There are given that the two points are:

`(-4,5)\text{ and }(2,1)`

Step-by-step explanation:

To find the equation, first, we need to find the slope of the line from the given points.

So,

From the formula of slope:

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

Where,

`x_1=-4,y_1=5,x_2=2,y_2=1`

Then,

Put all the values into the above formula:

So,

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(1-5)/(2+4) \\ m=-(4)/(6) \\ m=-(2)/(3) \end{gathered}`

Now,

From the formula of point-slope form:

`y-y_1=m(x-x_1)`

Then,

`\begin{gathered} y-y_(1)=m(x-x_(1)) \\ y-5=-(2)/(3)(x-(-4)) \\ y-5=-(2)/(3)(x+4) \\ 3y-15=-2(x+4) \end{gathered}`

Then,

`\begin{gathered} 3y-15=-2(x+4) \\ 3y-15=-2x-8 \\ 3y-15+2x+8=0 \\ 3y+2x-7=0 \\ 3y=-2x+7 \\ y=-(2)/(3)x+(7)/(3) \end{gathered}`

Final answer:

Hence, the equation of line is shown below:

`y=-(2)/(3)x+(7)/(3)`