Respuesta :

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

[tex]y=mx+b[/tex]

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

So, given the points:

[tex]\begin{gathered} \mleft(-4,3\mright) \\ \mleft(3,1\mright) \end{gathered}[/tex]

You can find the slope by using this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case, you can set up that.

[tex]\begin{gathered} y_2=3 \\ y_1=1 \\ \\ x_2=-4 \\ x_1=3 \end{gathered}[/tex]

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

[tex]m=\frac{3-1}{-4-3}=\frac{2}{-7}=-\frac{2}{7}[/tex]

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

[tex]y=mx+b[/tex]

Then, substituting the coordinates of the point:

[tex](3,1)[/tex]

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

[tex]\begin{gathered} 1=(-\frac{2}{7})(3)+b \\ \\ 1=-\frac{6}{7}+b \\ \\ 1+\frac{6}{7}=b \\ \\ b=\frac{13}{7} \end{gathered}[/tex]

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

[tex]\begin{gathered} y=mx+b \\ \\ y=-\frac{2}{7}x+\frac{13}{7} \end{gathered}[/tex]

The answer is:

[tex]y=-\frac{2}{7}x+\frac{13}{7}[/tex]

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