What is an equation of the line that passes through the points left bracket, minus, 5, comma, minus, 1, right bracket(−5,−1) and left bracket, 5, comma, minus, 3, right bracket(5,−3)?
To find the equation of the line passing through the points (-5, -1) and (5, -3), we can follow these steps:
1. Find the slope (m) of the line using the formula:
m = (y2 - y1)/(x2 - x1)
Let's use (-5, -1) as (x1, y1) and (5, -3) as (x2, y2):
m = (-3 - (-1))/(5 - (-5)) = (-3 + 1)/(5 + 5) = -2/10 = -1/5
2. Use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
Let's use (-5, -1) as (x1, y1) and m = -1/5:
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)
y + 1 = (-1/5)x - 1
y = (-1/5)x - 1 - 1
y = (-1/5)x - 2
Therefore, the equation of the line passing through the points (-5, -1) and (5, -3) is y = (-1/5)x - 2.
To find the equation of a line that passes through two given points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let's calculate the slope (m) using the given points (-5, -1) and (5, -3):
m = (-3 - (-1)) / (5 - (-5))
m = (-3 + 1) / (5 + 5)
m = -2 / 10
m = -1/5
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Let's use the first given point (-5, -1) to find the equation:
y - (-1) = -1/5(x - (-5))
y + 1 = -1/5(x + 5)
Simplifying the equation:
y + 1 = -1/5x - 1
y = -1/5x - 2
Therefore, the equation of the line that passes through the points (-5, -1) and (5, -3) is y = -1/5x - 2.
To find the equation of the line that passes through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where (x1, y1) represents one of the points, and m is the slope of the line.
First, let's find the slope (m) using the given points (-5, -1) and (5, -3).
m = (y2 - y1) / (x2 - x1)
m = (-3 - (-1)) / (5 - (-5))
m = (-3 + 1) / (5 + 5)
m = -2 / 10
m = -1/5
Now that we have the slope, we can choose any of the given points, let's use (-5, -1), and substitute the values into the point-slope form:
y - y1 = m(x - x1)
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)
This equation can be simplified further:
y + 1 = (-1/5)(x + 5)
y + 1 = (-1/5)(x) - (1/5)(5)
y + 1 = (-1/5)x - 1
y = (-1/5)x - 1 - 1
y = (-1/5)x - 2
Therefore, the equation of the line that passes through the points (-5, -1) and (5, -3) is y = (-1/5)x - 2.