A line passes through (1, 7) and (2, 10). What is the equation of the line?

To find the equation of the line that passes through the points (1, 7) and (2, 10), we first need to determine the slope of the line. The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

Plugging in our points (1, 7) and (2, 10):

m = (10 – 7) / (2 – 1) = 3 / 1 = 3

Now that we have the slope, we can use the point-slope form of the line’s equation:

y – y₁ = m(x – x₁)

Using the point (1, 7):

y – 7 = 3(x – 1)

Expanding this gives:

y – 7 = 3x – 3

Add 7 to both sides:

y = 3x + 4

So, the equation of the line that passes through the points (1, 7) and (2, 10) is:

y = 3x + 4