Determine the equation of the line passing through (1, 2) and (3, 6) in slope- intercept form y = 4x - 1; y = - x - 1; u = x + 1; y = x - 4
To find the equation of the line passing through two given points (x₁, y₁) and (x₂, y₂), we 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.
First, we need to find the slope (m) of the line. The slope is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (1, 2) and (3, 6), we can calculate the slope:
m = (6 - 2) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope, we can substitute it into the slope-intercept form equation with the coordinates of one of the points. Let's use the point (1, 2):
y = mx + b
2 = 2(1) + b
2 = 2 + b
b = 2 - 2
b = 0
Therefore, the equation of the line passing through (1, 2) and (3, 6) in slope-intercept form is y = 2x.