Given the coordinates (1, 5) and (4, 11).
The slope of the line that passes through the coordinates is
.
Fill in the blanks to write the equation of the line in point-slope form.
(
)
The slope of the line that passes through the coordinates (1, 5) and (4, 11) can be found using the formula:
slope = (change in y)/(change in x)
Let's calculate the change in y:
change in y = 11 - 5 = 6
Now, let's calculate the change in x:
change in x = 4 - 1 = 3
Therefore, the slope of the line passing through the coordinates is:
slope = 6/3 = 2.
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope.
Using the point (1, 5) and the slope 2, we can now fill in the blanks in the equation:
(y - 5) = 2(x - 1)