What is the equation of the line that passes through the points (2, 1) and (4, 5)?

To find the equation of the line that passes through the points (2, 1) and (4, 5), we can use the slope-intercept form of the line, which is given by:

y = mx + b

where m is the slope and b is the y-intercept. First, we need to calculate the slope (m) of the line using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

Here, let:

• (x₁, y₁) = (2, 1)
• (x₂, y₂) = (4, 5)

Substituting the points into the slope formula:

m = (5 – 1) / (4 – 2) = 4 / 2 = 2

Now that we have the slope, we can find the y-intercept (b). We will use one of the points; let’s use (2, 1):

1 = 2(2) + b

Now solve for b:

1 = 4 + b

b = 1 – 4 = -3

Now that we have both m and b, we can write the equation of the line:

y = 2x – 3

In conclusion, the equation of the line that passes through the points (2, 1) and (4, 5) is:

y = 2x – 3

This equation tells us that for every increase of 1 in x, y increases by 2, starting from a y-intercept of -3 on the y-axis.