find an equation of the line contaning the given pair of points.
(2,4) and (6,5)
is this correct i got y=1 over 4x + 2
The easiest way to check is to substitute the x values into the equation and see if you get the corresponding y values.
y = 1/(4x + 2) is not a straight line, and does not contain either point.
What you perhaps meant was
y = (1/4)x + 2
That has the right slope, but does not go through either point.
The correct answer is
y = (1/4)x + (7/2)
To find the equation of the line containing the given pair of points (2,4) and (6,5), we can use the point-slope form of a linear equation, which is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents one point on the line and 'm' represents the slope of the line.
First, we need to find the slope (m). The slope can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates of the given points, we can substitute the values into the formula:
m = (5 - 4) / (6 - 2)
m = 1 / 4
Now that we have the slope, we can choose either of the given points (let's use (2,4)) and substitute its coordinates, along with the slope, into the point-slope form equation:
y - 4 = (1/4)(x - 2)
Simplifying this equation, we get:
y - 4 = (1/4)x - 1/2
To isolate y, we can add 4 to both sides of the equation:
y = (1/4)x - 1/2 + 4
y = (1/4)x + 7/2
Therefore, the equation of the line containing the points (2,4) and (6,5) is y = (1/4)x + 7/2.