Write an equation that goes through (1,-2) and is parallel to y + 2=3 (x - 1)

y = 3x - 5

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+b, where m is the gradient and b is the y-intercept.

Let's rewrite the equation of the given line in the form of y=mx+b, so we can find its gradient.

y + 2 = 3 (x - 1)

y + 2 = 3x - 3 (expand)

y = 3x - 3 - 2

y = 3x - 5

Gradient of given line = 3

Gradient of unknown line = 3,

since parallel lines have the same gradient.

Susbt. m=3 into the equation:

y = 3x + b

Substitute a coordinate to find the value of b.

When x = 1, y = - 2,

-2 = 3 (1) + b

-2 = 3 + b

b = - 2 - 3 (-3 on both sides)

b = - 5 (simplify)

Thus the equation of the line is y = 3x - 5.