Question

(3, −4) and (4, −a) lie on line. Find a?

Hint:

Remember: When two points lie on the same straight line, the slope between them is constant.

Answer 1

Step 1: Use the formula for the slope of a line.
The points (3, −4) and (4, −a) lie on the same straight line. The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the given points (3, −4) and (4, −a) into the formula: \[ m = \frac{-a - (-4)}{4 - 3} = \frac{-a + 4}{1} = 4 - a \]
Step 2: Use the condition for points on the same line.
Since the points lie on the same line, their slope must be the same. Now, calculate the slope using the coordinates of the first point (3, −4) and the second point (4, −a). \[ m = \frac{-a + 4}{1} = 4 - a \]