Finding the equation of a line when you have two points is a straightforward process. The general equation of a line can be expressed in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To begin, let’s say the two points you are given are (x1, y1) and (x2, y2). The first step is to calculate the slope (m) of the line that passes through these points. The formula for the slope is:
m = (y2 – y1) / (x2 – x1)
Once you have calculated the slope, you can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b). Using the point (x1, y1), you would rearrange the formula:
b = y1 – mx1
Now, with both m and b known, you can write the equation of the line in the form y = mx + b.
For example, let’s say the points are (1, 2) and (3, 4). First, we calculate the slope:
m = (4 – 2) / (3 – 1) = 2 / 2 = 1
Next, using the point (1, 2) to find b:
b = 2 – (1 * 1) = 2 – 1 = 1
Now, substituting m and b into the slope-intercept equation gives us:
y = 1x + 1 or simply y = x + 1.
And that’s how you can find the equation of a line when you’re given two points!