Question

Match the equation of the line passing through (3,-2) with the conditions given

• A. x + y = 1
• B. y = 3x – 11
• C. y = x – 5
• D. 2x
  ]\ 3y = 0

Answer 1

The line must pass through the point (3,-2)

Condition 1:
The line is perpendicular to y = x.
Slope of the line y = x is 1.
If the equation of the required line is y = mx + c, then the slope of the required line is m.
Then, $m\times 1=-1$, or m = -1
y = -x + c
Also, the line passes through (3,-2)
Then, -2 = -3 + c. Or, c = 1
Thus, the required line is y = -x + 1. Or, x + y = 1

Condition 2:
The line is parallel to y = 3x - 11.
Slope of the line y = x is 3.
If the equation of the required line is y = mx + c, then the slope of the required line is m.
Then, m = 3
y = 3x + c
Also, the line passes through (3,-2)
Then, $-2=3\times 3+c$. Or, c = -11
Thus, the required line is y = 3x – 11.

Condition 3:
Y-intercept of the line is –5
Let the equation of the required line be y = mx + c.
Then, c = –5.
Thus, the line is y = mx – 5.
Also, the line passes through (3,-2)
Then, -2 = 3m –5.
3 = 3m. Or, m =1
Thus, the equation of the required line is y = x – 5.

Condition 4:
Line passes through (0,0).
Slope of the line = $\frac{-2-0}{3-0}=\frac{-2}{3}$
Thus, the equation of the line is $y-0=-\frac{2}{3}(x-0)$
Or, $y=-\frac{2}{3}x$
Or, 2x + 3y = 0.