Calculating Slope Using Coordinates
The slope ($m$) of a straight line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$ m = \frac{y_2 - y_1}{x_2 - x_1} $
Applying the Slope Formula
We are given two points, $(4, p)$ and $(0, q)$, and the slope $m = \frac{3}{4}$. Let $(x_1, y_1) = (4, p)$ and $(x_2, y_2) = (0, q)$.
Substitute these values into the slope formula:
$ \frac{3}{4} = \frac{q - p}{0 - 4} $
Solving for $(p - q)$
Simplify the denominator:
$ \frac{3}{4} = \frac{q - p}{-4} $
To solve for $(q - p)$, multiply both sides by $-4$:
$ (q - p) = \frac{3}{4} \times (-4) $
$ q - p = -3 $
The question asks for the value of $(p - q)$. Since $(q - p) = -3$, we can find $(p - q)$ by multiplying by $-1$:
$ p - q = -(q - p) $
$ p - q = -(-3) $
$ p - q = 3 $
Therefore, the value of $(p – q)$ is $3$. The correct option is C.
Important Questions from Algebra
- For positive non-zero real variables $x$ and $y$, if
$ln\left(\frac{x+y}{2}\right) = \frac{1}{2} [ln\left(x\right) + ln\left(y\right)]$
then, the value of $\frac{x}{y} + \frac{y}{x}$ is Given $f(x, y) = x^2 - 2xy + y^2$
The complete contour of the equation $f(x, y) = 1$ is described by the option(s) ___.
- It is given that $x$ and $y$ are integers in the following equation:
$$(x + y - 7)^2 + (y + 3x - 13)^2 = 0$$
The value of $(x^3 + y^3)$ is ________ (in integer). - If $pqr \neq 0$ and $p^{-x} = \frac{1}{q}$, $q^{-y} = \frac{1}{r}$, $r^{-z} = \frac{1}{p}$, what is the value of the product $xyz$?
- If $Pe^x = Qe^{-x}$ for all real values of $x$, which one of the following statements is true?
