Respuesta :
We are asked to find the equation of the line in slope-intercept form that passes through the following points.
[tex](5,-6)\text{ and }(25,10)[/tex]Recall that the equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of the line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{Where (}x_1,y_1)=(5,-6)\text{ and (}x_2,y_2)=(25,10)[/tex]Let us substitute the given values into the slope formula
[tex]m=\frac{10-(-6)}{25-5}=\frac{10+6}{20}=\frac{16}{20}=\frac{4}{5}=0.8[/tex]So the equation of line at this point is
[tex]y=0.8x+b[/tex]Now let us find the y-intercept (b)
Choose any one point from the given two points
Let choose (5, -6) and substitute it into the above equation
[tex]\begin{gathered} -6=0.8(5)+b \\ -6=4+b \\ b=-6-4 \\ b=-10 \end{gathered}[/tex]Therefore, now we got both slope and y-intercept
So the equation of the line in slope-intercept form is
[tex]y=0.8x-10[/tex]Option (A) is correct.
