Find an equation of the line containing the given pair of points.
(4,1) and (12,6)
To find the equation of the line containing the given pair of points, we can use the formula for the equation of a line in slope-intercept form: y = mx + b.
First, let's find the slope (m) of the line using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) = (4, 1) and (x2, y2) = (12, 6):
m = (6 - 1)/(12 - 4) = 5/8
Now that we have the slope, we can choose one of the given points (let's use (4, 1)) and substitute it into the equation y = mx + b to find the y-intercept (b):
1 = (5/8)(4) + b
1 = 20/8 + b
1 = 5/2 + b
1 - 5/2 = b
-3/2 = b
So the y-intercept (b) is -3/2.
Now we can write the equation of the line y = mx + b using the slope (m = 5/8) and the y-intercept (b = -3/2):
y = (5/8)x - 3/2
Therefore, the equation of the line containing the given pair of points (4, 1) and (12, 6) is y = (5/8)x - 3/2.
To find the equation of a line containing two points, we can use the point-slope equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents one point on the line and m is the slope of the line.
Let's denote the first point as (x₁, y₁) = (4, 1) and the second point as (x₂, y₂) = (12, 6).
First, we need to find the slope (m) of the line:
m = (y₂ - y₁) / (x₂ - x₁)
= (6 - 1) / (12 - 4)
= 5 / 8
So, the slope of the line is 5/8.
Now, let's use the point-slope equation with the first point:
y - 1 = (5/8)(x - 4)
Distributing the slope:
y - 1 = (5/8)x - (5/8)(4)
y - 1 = (5/8)x - 5/2
Adding 1 to both sides to isolate y:
y = (5/8)x - 5/2 + 1
y = (5/8)x - 5/2 + 2/2
y = (5/8)x - 5/2 + 2/2
y = (5/8)x - 3/2
Therefore, the equation of the line passing through the points (4, 1) and (12, 6) is y = (5/8)x - 3/2.
To find the equation of the line containing the given pair of points, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
(y - y1) = m(x - x1)
Where (x1, y1) is one of the given points, and m is the slope of the line.
Let's calculate the slope (m) using the two given points. The slope (m) is defined as the ratio of the change in y-coordinates to the change in x-coordinates between the two points.
m = (y2 - y1) / (x2 - x1)
Using the given points (4,1) and (12,6), we can substitute the values into the formula:
m = (6 - 1) / (12 - 4)
m = 5 / 8
Now that we have the slope (m), we can use one of the given points to write the equation using the point-slope form.
Let's use the point (4,1):
(y - 1) = (5/8)(x - 4)
Simplifying this equation, we get:
y - 1 = (5/8)x - 20/8
y - 1 = (5/8)x - 5/2
Finally, we can rewrite the equation in the standard form:
(5/8)x - y = 5/2 - 1
(5/8)x - y = 5/2 - 2/2
(5/8)x - y = 3/2
Therefore, the equation of the line containing the given pair of points is:
(5/8)x - y = 3/2