Question

The graph of 4x + 2y= 5 cuts the x axis at point A and the y axis at point B. Find the:

Coordinates of point A.

Gradient of line A B.

Answer 1

At the x-axis, the y value is zero, so let y = 0
4x + 0 = 5
x = 5/4 , so point A is (5/4 , 0)
At the y-axis, the x value is zero, so let x = 0
0 + 2y = 5
y = 5/2 , so point B is (0 , 5/2)

slope = (5/2-0)/(0 - 5/4) = 2

other way:
if you have a linear equation of the form x/a + y/b = 1
then a is the x-intercept, and b is the y-intercept and the slope is b/a

4x+ 2y = 5
divide each term by 5
4x/5 + 2y/5 = 1
x/(5/4) + y/(5/2) = 1 , see the intercepts ?
slope = (5/2) / (5/4) = (5/2)(4/5) = 2

Answer 2

Draw the graph of the line represent by the equation