How to Write an Equation of the Line That Passes Through the Given Points

To write the equation of a line that passes through two given points, you need to follow a few steps.

First, identify the coordinates of the two points. Let’s say these points are (x₁, y₁) and (x₂, y₂). For example, consider the points (2, 3) and (4, 7).

Next, calculate the slope (m) of the line using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

For our points, this would be:

m = (7 – 3) / (4 – 2) = 4 / 2 = 2

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

y – y₁ = m(x – x₁)

Using our slope of 2 and the point (2, 3):

y – 3 = 2(x – 2)

Distributing the slope through:

y – 3 = 2x – 4

Now, add 3 to both sides to solve for y:

y = 2x – 1

This gives you the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Thus, the equation of the line that passes through the points (2, 3) and (4, 7) is:

y = 2x – 1

In summary, the steps to find the equation of a line through two points are to find the slope using the points’ coordinates, and then use either point-slope or slope-intercept form to write out the equation.