Question

The gradient of a line passing through the points ( M(3, y) ) and ( N(x, -5) ) is ( )(-7)(8) ). Find the value of ( x ) and ( y ).

a) ( x = ) 26/3 ), ( y = ) 19/3 )

b) ( x = ) 3/26 ), ( y = -) 19/3 )

c) ( x = -) 26/3 ), ( y = ) 19/3 )

d) ( x = ) 26/3 ), ( y = -) 19/3 )

Answer 1

To find the value of x and y, we can use the formula for the gradient of a line passing through two points.

Step-by-step explanation:

To find the gradient (slope) of a line passing through two points, you can use the formula:

m = (y2 - y1) / (x2 - x1)

Given the points (M(3, y)) and (N(x, -5)), we can substitute the coordinates into the formula:

m = (y - (-5)) / (x - 3)

Since the given gradient is -7, we can set that equal to the formula:

-7 = (y - (-5)) / (x - 3)

Solving for y, we find y = -7x + 26. Substituting this value back into the formula, we get:

-7 = (-7x + 26 - (-5)) / (x - 3)

Simplifying and solving for x, we find x = 26/3. Substituting x = 26/3 into the equation for y, we find y = 19/3.