find an equationof the line containing the given pair of points (2,4) (6,5)
To find the equation of a line containing two given points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where "m" represents the slope of the line, and "b" represents the y-intercept.
Step 1: Find the slope (m):
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (2, 4) and (6, 5), we can substitute the values into the formula:
m = (5 - 4) / (6 - 2)
m = 1 / 4
m = 0.25
Step 2: Find the y-intercept (b):
To find the y-intercept (b), we can select one of the given points and substitute its coordinates into the equation:
Using the point (2, 4):
y = mx + b
4 = 0.25 * 2 + b
4 = 0.5 + b
b = 4 - 0.5
b = 3.5
Step 3: Write the equation:
Now that we have the slope (m = 0.25) and the y-intercept (b = 3.5), we can write the equation of the line:
y = 0.25x + 3.5
Therefore, the equation of the line containing the given points (2, 4) and (6, 5) is y = 0.25x + 3.5.