We can find the x-intercept of a line by replacing 0 for y and solving for x, like this:
2(y - 3x) = 10 - 4x
2(0 - 3x) = 10 - 4x
2(3x) = 10 - 4x
6x = 10 - 4x
6x + 4x = 10 - 4x + 4x
10x = 10
10x/10 = 10/10
x = 1
Then, the intercept of the given line on the x-axis is (1, 0)
Similarly, in order to find the intercept with the y-axis, we just have to replace 0 for x and solve for y, like this:
2(y - 3(0)) = 10 - 4x(0)
2(y - 0) = 10 - 0
2y = 10
2y/2 = 10/2
y = 5
Then, the intercept of the given line on the y-axis is (0, 5)
In order to find the gradient of the line, we can rewrite the original equation to the form y=mx+b, where m is the gradient. We can do this like this:
2(y - 3x) = 10 - 4x
2y - 2(3x) = 10 - 4x
2y - 6x = 10 - 4x
2y - 6x + 6x = 10 - 4x + 6x
2y = 10 + 2x
2y/2 = (10 + 2x)/2
y = 5 + x
Then, the gradient of the given line equals 1