Respuesta :

Explanation:

The equation of a line in slope-intercept form is:

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

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

The formula for the slope of a line with points (x1, y1) and (x2, y2) is:

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

In this case the slope is:

[tex]m=\frac{-4-2}{3-1}=\frac{-6}{2}=-3[/tex]

For now we have:

[tex]y=-3x+b[/tex]

To find the y-intercept b, we have to replace (x,y) for one of the given points and solve for b. If we use point (1,2):

[tex]\begin{gathered} y=-3x+b \\ \text{ replacing x = 1 and y = 2} \\ 2=-3\cdot1+b \\ 2=-3+b \\ b=2+3=5 \end{gathered}[/tex]

Answer:

The equation of the line is: y = -3x + 5