Question

The equation of the straight line parallel to y=-3x and passing through the point (3,-2) is

• A. y=-3x+7
• B. y=-3x+9
• C. y=-3x+11
• D. y=-3x-7
• E. y=-3x+11

Answer 1

The Correct Option is A

The equation of a straight line is given by: \[ y = mx + c, \] where \( m \) is the slope and \( c \) is the y-intercept.
The line we are given, \( y = -3x \), has a slope of \( m = -3 \).
Since the required line is parallel to this line, it will have the same slope, i.e., \( m = -3 \).
Now, we are given that this line passes through the point \( (3, -2) \).
We can substitute \( x = 3 \) and \( y = -2 \) into the equation of the line \( y = mx + c \) to find the value of \( c \), the y-intercept.
Substitute \( m = -3 \), \( x = 3 \), and \( y = -2 \) into the equation: \[ -2 = -3(3) + c. \] Simplifying: \[ -2 = -9 + c \quad \Rightarrow \quad c = -2 + 9 = 7. \] Thus, the equation of the line is: \[ y = -3x + 7. \]

The correct option is (A) : \(y=-3x+7\)

Answer 2

We are given the line \(y = -3x\) and the point \((3, -2)\).

Since the line we want is parallel to \(y = -3x\), it will have the same slope, which is \(m = -3\).

The equation of a line with slope \(m\) passing through a point \((x_1, y_1)\) is given by \(y - y_1 = m(x - x_1)\).

In our case, \(m = -3\) and \((x_1, y_1) = (3, -2)\). So, we have \(y - (-2) = -3(x - 3)\).

Simplifying the equation, we get:

\(y + 2 = -3x + 9\)

Solving for \(y\), we have:

\(y = -3x + 9 - 2\)

\(y = -3x + 7\)

Therefore, the equation of the line is \(y = -3x + 7\).