Question

Find the equation (in terms of x) of the line through the points (-4,3) and (3,1)y =

Answer 1

The Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

So, given the points:

`\begin{gathered} \mleft(-4,3\mright) \\ \mleft(3,1\mright) \end{gathered}`

You can find the slope by using this formula:

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

In this case, you can set up that.

`\begin{gathered} y_2=3 \\ y_1=1 \\ \\ x_2=-4 \\ x_1=3 \end{gathered}`

Then, substituting values into the formula and evaluating, you get:

`m=(3-1)/(-4-3)=(2)/(-7)=-(2)/(7)`

Now you can substitute the slope of the line and the coordinate of one of the points given in the exercise, into the equation

`y=mx+b`

Then, substituting the coordinates of the point:

`(3,1)`

And then solving for "b", you get that this is:

`\begin{gathered} 1=(-(2)/(7))(3)+b \\ \\ 1=-(6)/(7)+b \\ \\ 1+(6)/(7)=b \\ \\ b=(13)/(7) \end{gathered}`

Finally, knowing "m" and "b", you can determine that the equation of this line (in terms of "x"), is:

`\begin{gathered} y=mx+b \\ \\ y=-(2)/(7)x+(13)/(7) \end{gathered}`

The answer is:

`y=-(2)/(7)x+(13)/(7)`