The slope-intercept equation is:
[tex]y=m\cdot x+b,[/tex]
where m is the slope and b is the value of the y-intercept.
The point-slope equation is:
[tex]y=m\cdot(x-x_0)+y_0,[/tex]
where m is the slope and (x0,y0) are the coordinates of one point of the line.
From the graph of the line, we see that it passes through the points:
• (x0,y0) = (2,0),
,
• (x1,y1) = (0,-5).
The slope of the line is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}=\frac{-5-0}{0-2}=\frac{5}{2}\text{.}[/tex]
The value of the y-intercept b is the value of y when x = 0, so in this case, we have:
[tex]b=-5.[/tex]
Replacing the values obtained of m, b and (x0,y0) in the equations above, we find that:
• The, slope-intercept, equation is:
[tex]y=\frac{5}{2}\cdot x-5[/tex]
• The ,point-slope, equation is:
[tex]y=\frac{5}{2}\cdot(x-2)[/tex]
