Question

The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.

Answer 1

The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.

Gradient is the slope

So the slope of the line joining the points A(3,-5) and B(6,k) is 4

Slope of line joining two points = $\frac{y_2-y_1}{x_2-x_1}$

A(3,-5) and B(6,k) are (x1,y1)  and (x2,y2)

slope = $\frac{y_2-y_1}{x_2-x_1}$

slope = $\frac{k-(-5)}{6-3}=\frac{k+5)}{3}$

We know slope =4

 $\frac{k+5)}{3}=4$

Cross multiply  and solve for k

k + 5 = 12

k = 7

The value of k = 7