Question

What is an equation, in standard form, of the line through (1, 7) and (−2, −3)?

Answer 1

To find the equation of the line through two points, you can use the formula:

(y - y₁) = m(x - x₁)

Where (x₁, y₁) and (x, y) are the coordinates of the points, and m is the slope of the line.

First, let's find the slope of the line:

m = (y₂ - y₁) / (x₂ - x₁)

m = (-3 - 7) / (-2 - 1)

m = (-3 - 7) / (-3)

m = (-10) / (-3)

m = 10/3

Now, we have the slope, we can plug in the values of one of the points (1, 7) into the formula:

(y - 7) = (10/3)(x - 1)

To write the equation in standard form, we need to eliminate the fraction by multiplying through by 3:

3(y - 7) = 10(x - 1)

Expanding both sides:

3y - 21 = 10x - 10

Rearranging the equation to bring it into standard form (Ax + By = C), we get:

10x - 3y = -11

So the equation of the line in standard form through (1, 7) and (-2, -3) is 10x - 3y = -11.