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)?
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
To find the equation of the line that passes through two points, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b,
where m is the slope of the line, and b is the y-intercept.
Step 1: Find the slope (m) of the line using the two given points.
The formula to find the slope between two points is:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (-1, -6) and (6, 1):
m = (1 - (-6)) / (6 - (-1))
m = 7 / 7
m = 1.
Step 2: Use one of the points and the slope to find the y-intercept.
Let's use the point (-1, -6) and the slope (m = 1) in the slope-intercept form:
y = mx + b,
-6 = 1*(-1) + b
-6 = -1 + b
b = -5.
Step 3: Write the equation of the line.
Using the slope-intercept form, the equation of the line passing through the points (-1, -6) and (6, 1) is:
y = 1x - 5,
which simplifies to:
y = x - 5.
To find the equation of a 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) are the coordinates of one point on the line, and m is the slope of the line.
First, we need to find the slope (m) using the two given points. The slope between two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (-1, -6) and (6, 1):
m = (1 - (-6)) / (6 - (-1))
= (1 + 6) / (6 + 1)
= 7 / 7
= 1
So, the slope of the line passing through the given points is 1.
Now that we have the slope, we can choose either of the two points (let's use (-1, -6)) and substitute it into the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - (-6) = 1(x - (-1))
y + 6 = x + 1
Simplifying the equation gives us the equation of the line:
y = x - 5
Therefore, the equation of the line passing through the points (-1, -6) and (6, 1) is y = x - 5.