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Find the gradient and the intercepts on the x and y axes of a straight line with a given equation 2(y-3x)=10-4x

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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

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