Question 9:
Find the equation of the line(s) through (2, -2). If the sum of the intercepts is 3.
Given:
(x1, y1) ==> (2, -2)
Sum of intercepts = 3
To find the equation, we have:
x + y = 3
Subtract y from both sides:
x + y - y = 3 - y
x = 3 - y
Use the slope-intercept form:
y = mx + b
Substitute b for 3:
y = mx + 3
Substitute x for 2 and y for -2:
-2 = m(2) + 3
Let's find the slope m:
-2 = 2m + 3
Subtract 3 from both sides:
-2 - 3 = 2m + 3 - 3
-5 = 2m
Divide both sides by 2:
[tex]\begin{gathered} -\frac{5}{2}=\frac{2m}{2} \\ \\ m=-\frac{5}{2} \end{gathered}[/tex]
Now, we have:
[tex]y=-\frac{5}{2}x+3[/tex]
