(2,4) and (5,8)
The given points are (2,4) and (5,8).
The x-coordinate of the first point is 2, and the y-coordinate is 4.
The x-coordinate of the second point is 5, and the y-coordinate is 8.
To find the equation of a line passing through the points (2,4) and (5,8), you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Given points: (2,4) and (5,8)
Using the formula: m = (8 - 4) / (5 - 2)
Simplifying: m = 4 / 3
So, the slope (m) is 4/3.
Step 2: Use the point-slope formula to find the equation: y - y1 = m(x - x1)
Using the point (2,4) and the slope 4/3:
y - 4 = (4/3)(x - 2)
y - 4 = (4/3)x - (4/3)(2)
y - 4 = (4/3)x - 8/3
Step 3: Simplify the equation:
Multiply both sides of the equation by 3 to eliminate the fraction:
3y - 12 = 4x - 8
Move the constant term to the other side of the equation:
3y = 4x - 8 + 12
3y = 4x + 4
Therefore, the equation of the line passing through the points (2,4) and (5,8) is 3y = 4x + 4.
It appears that you have mentioned two points: (2,4) and (5,8). These points represent coordinates on a Cartesian plane. To understand the relationship between these points, we can calculate the slope of the line passing through them.
To find the slope, we can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let's label the first point (x1, y1) as (2,4) and the second point (x2, y2) as (5,8).
Substituting the values into the formula, we get:
slope (m) = (8 - 4) / (5 - 2)
= 4 / 3
So, the slope between the points (2,4) and (5,8) is 4/3.
The slope of a line represents the rate of change between two points on that line. In this case, for every increase of 3 units in the x-coordinate, the y-coordinate increases by 4 units.
It is important to note that the slope alone does not determine the equation of the line passing through these points. Additional information, such as the y-intercept or another point, is required to determine the equation of the line.