Given:
A line passes through the points (1,-7) and (5,-25).
To find:
The y-intercept of the line.
Solution:
The line passes through the points (1-7) and (5-25). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-7)=\dfrac{-25-(-7)}{5-1}(x-1)[/tex]
[tex]y+7=\dfrac{-25+7}{4}(x-1)[/tex]
[tex]y+7=\dfrac{-18}{4}(x-1)[/tex]
[tex]y+7=-4.5(x-1)[/tex]
Subtracting 7 from both sides, we get
[tex]y=-4.5x+4.5-7[/tex]
[tex]y=-4.5x-2.5[/tex]
Putting x=0, we get
[tex]y=-4.5(0)-2.5[/tex]
[tex]y=0-2.5[/tex]
[tex]y=-2.5[/tex]
Therefore, the y-intercept of the given line is -2.5 and the vertex form of (0,-2.5).
