Question

A perpendicular passes through (2.4) and meets a line at (3.-). Find the expans - 7. A perpendicular from the origin meets a line at (4,-5), find the equation of the 9. Find the equation(s) of the line(s) through (2,-2) if the sum of the intercepts is 3. (a) perpendicular solute (b) line (a) perpendicular (b) line 8. - Find the value of a ifax - 9y = 6 is parallel to x - ay = 5. Find the anple that line 1, makes with line 1Question 9

Answer 1

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:

`\begin{gathered} -(5)/(2)=(2m)/(2) \\ \\ m=-(5)/(2) \end{gathered}`

Now, we have:

`y=-(5)/(2)x+3`