Question

What is an equation of the line that passes through the points left bracket, minus, 1, comma, minus, 6, right bracket(−1,−6) and left bracket, 6, comma, 1, right bracket(6,1)?

Answer 1

To find the equation of the line passing through the points (-1,-6) and (6,1), we need to find the slope of the line.

The slope (m) of a line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-1,-6) and (6,1), the slope (m) can be calculated as:

m = (1 - (-6)) / (6 - (-1))
m = 7 / 7
m = 1

So, the slope (m) of the line passing through (-1,-6) and (6,1) is 1.

Now we can use the slope-intercept form of a linear equation, y = mx + b, to find the equation of the line.

Let's substitute the coordinates of one of the points, (-1,-6), into the equation to find the y-intercept (b).

-6 = 1(-1) + b
-6 = -1 + b
b = -6 + 1
b = -5

The y-intercept (b) of the line passing through (-1,-6) and (6,1) is -5.

Therefore, the equation of the line is:
y = 1x - 5
or simplified as:
y = x - 5