Simplify (x−5)/6 − 6/(x−5) (b) Find the gradient of a line joining the points A(−4,−6) and B(6,8).

Step 1: Identify the coordinates of the two given points. Let point A be (x₁, y₁) = (−4, −6). Let point B be (x₂, y₂) = (6, 8). Step 2: Use the formula for the gradient (slope) of a line, m = (y₂ − y₁)/(x₂ − x₁). m = (8 − (−6))/(6 − (−4)) Step 3: Simplify the expression. m = (8 + 6)/(6 + 4); m = 14/10; m = 7/5 The gradient of the line joining points A and B is: 7/5

Simplify (x−5)/6 − 6/(x−5) (b) Find the gradient of a line joining the points A(−4,−6) and B(6,8).

Step 1: Identify the coordinates of the two given points. Let point A be (x₁, y₁) = (−4, −6). Let point B be (x₂, y₂) = (6, 8). Step 2: Use the formula for the gradient (slope) of a line, m = (y₂ − y₁)/(x₂ − x₁). m = (8 − (−6))/(6 − (−4)) Step 3: Simplify the expression. m = (8 + 6)/(6 + 4); m = 14/10; m = 7/5 The gradient of the line joining points A and B is: 7/5

Solved: Simplify (x−5)/6 − 6/(x−5) (b) Find the gradient of…

Identify the coordinates of the two given points.
Let point A be $(x_1, y_1) = (-4, -6)$ .
Let point B be $(x_2, y_2) = (6, 8)$ .
Use the formula for the gradient (slope) of a line, $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
$m = \frac{8 - (-6)}{6 - (-4)}$
Simplify the expression.
$m = \frac{8 + 6}{6 + 4}$ $m = \frac{14}{10}$ $m = \frac{7}{5}$
The gradient of the line joining points A and B is:
$\frac{7}{5}$

Simplify (x-5)/6 - 6/(x-5) (b) Find the gradient of a line joining the points A(-4,-6) and B(6,8).

Answer

Step-by-step solution

Identify the coordinates of the two given points.

Use the formula for the gradient (slope) of a line, $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Simplify the expression.

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