Question

Write in standard form: An equation of a line which has a slope of 2/3 and contains the point (0,2)

Answer 1

The equation of a line with slope 2/3 and point (0,2) is 3y - 2x = 6

The equation of a line is given as

$y = mx + c$

m = slope

c = intercept

The data given are

• slope (m) = 2/3
• x = 0
• y = 2

Intercept

Put in the values into the equation above and solve for the intercept.

$y = mx + c\\2 = 2/3(0) + c\\c = 2$

Equation of the line

$y = 2/3x +2$

Multiply through by 3

$y = 2/3(x) +2\\y(3) = (3)2/3x + 2(3)\\3y = 2x + 6\\3y - 2x = 6$

From the above calculation, the equation of a line is 3y - 2x = 6

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