The two lines $l x+my=n$ and $l'x+m'y=n'$ are perpendicular if
- ll'+mm'=0
- lm'+ml'
- lm+l'm'=0
- lm'+ml'=0
The Correct Option is A
Solution and Explanation
$? ll'' + mm' = 0$
Top Questions on Slope of a line
- Let the slope of the line \( 45x + 5y + 3 = 0 \) be \( 27r_1 + \frac{9r_2}{2} \) for some \( r_1, r_2 \in \mathbb{R} \).Then\[\lim_{x \to 3} \left( \int_3^x \frac{8t^2}{\frac{3r_1 x}{2} - r_2 x^2 - r_1 x^3 - 3x} \, dt \right)\]is equal to _____.
- JEE Main - 2024
- Mathematics
- Slope of a line
- A line passing through the point \( A(9, 0) \) makes an angle of \( 30^\circ \) with the positive direction of the x-axis. If this line is rotated about \( A \) through an angle of \( 15^\circ \) in the clockwise direction, then its equation in the new position is:
- JEE Main - 2024
- Mathematics
- Slope of a line
- Variance of 6, 7, 8, 9 is
- KEAM - 2024
- Mathematics
- Slope of a line
- If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is
- AP POLYCET - 2024
- Mathematics
- Slope of a line
- A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?
- KEAM - 2023
- Mathematics
- Slope of a line
Questions Asked in KCET exam
- A die is thrown 10 times. The probability that an odd number will come up at least once is:
- KCET - 2024
- Probability
- The incorrect statement about the Hall-Heroult process is:
- KCET - 2024
- General Principles and Processes of Isolation of Elements
- Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:
- KCET - 2024
- Linear Programming Problem
- If a random variable $X$ follows the binomial distribution with parameters $n = 5$, $p$, and $P(X = 2) = 9P(X = 3)$, then $p$ is equal to:
- KCET - 2024
- binomial distribution
- A random variable $X$ has the following probability distribution: \[ \begin{array}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & \frac{25}{36} & k & \frac{1}{36} \\ \hline \end{array} \] If the mean of the random variable $X$ is $\frac{1}{3}$, then the variance is:
- KCET - 2024
- Random Variables and its Probability Distributions
Concepts Used:
The Slope of a Line
A slope of a line is the conversion in y coordinate w.r.t. the conversion in x coordinate.
The net change in the y-coordinate is demonstrated by Δy and the net change in the x-coordinate is demonstrated by Δx.
Hence, the change in y-coordinate w.r.t. the change in x-coordinate is given by,
\(m = \frac{\text{change in y}}{\text{change in x}} = \frac{Δy}{Δx}\)
Where, “m” is the slope of a line.
The slope of the line can also be shown by
\(tan θ = \frac{Δy}{Δx}\)
Read More: Slope Formula
The slope of a Line Equation:
The equation for the slope of a line and the points are known to be a point-slope form of the equation of a straight line is given by:
\(y-y_1=m(x-x_1)\)
As long as the slope-intercept form the equation of the line is given by:
\(y = mx + b\)
Where, b is the y-intercept.