Given:
A line passing through the points (4,5) and (2,-6).
The objective is to find the equation of line in slope-intercept form.
Explanation:
Consider the given points as
[tex]\begin{gathered} (x_1,y_1)=(4,5) \\ (x_2,y_2)=(2,-6) \end{gathered}[/tex]The slope of the line can be calculated as,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{ . . . . . . .(1)}[/tex]To find slope m:
On plugging the gven vales in rquation of slope,
[tex]\begin{gathered} m=\frac{-6-5}{2-4} \\ m=\frac{-11}{-2} \\ m=\frac{11}{2} \end{gathered}[/tex]The general equation of straight line is,
[tex]y-y_1=m(x-x_1).......(2)_{}[/tex]To find equation:
On plugging the values in the above equation.
[tex]\begin{gathered} y-5=\frac{11}{2}(x-4) \\ y-5=\frac{11}{2}x-4(\frac{11}{2}) \\ y=\frac{11}{2}x-22+5 \\ y=\frac{11}{2}x-17 \end{gathered}[/tex]Hence, the equation of straight linne is y = (11/2)x - 17.
So the answer is correct.
