Q:

The line contains the point (9,-9) and has the same y-intercept as y + 1 = 4 (x - 2). Write the equation of this line in slope-intercept form.

Accepted Solution

A:
Answer:The equation for this line, in slope-intercept form, is given by:[tex]y = - 9[/tex]Step-by-step explanation:The equation of a line in the slope-intercept form has the following format:[tex]y = ax + b[/tex]In which a is the slope of the line and b is the y intercept.Solution:The line has the same y-intercept as [tex]y + 1 = 4 (x - 2)[/tex].So, we have to find the y-intercept of this equation[tex]y + 1 = 4 (x - 2)[/tex][tex]y = 4x - 8 - 1[/tex][tex]y = 4x - 9[/tex]This equation, has the y-intercept = -9. Since this line has the same intercept, we have that [tex]b=-9[/tex].Fow now, the equation of this line is[tex]y = ax - 9[/tex]The line contains the point [tex](9,-9)[/tex]This means that when [tex]x = 9, y = -9[/tex]. We replace this in the equation and find a[tex]y = ax - 9[/tex][tex]-9 = 9a - 9[/tex][tex]9a = 0[/tex][tex]a = \frac{0}{9}[/tex][tex]a = 0[/tex]The equation for this line, in slope-intercept form, is given by:[tex]y = - 9[/tex]