Write an equation in slope-intercept form, given that the line passes through the point (2,7) and has a slope of 2?
Coordinate Geometry is a very important topic in mathematics in which various equations are represented as curves on the cartesian, polar, or other types of planes.
Answer: The slope-intercept form equation of the line that passes through the point (2, 7) and has a slope of 2 is y = 2x + 3.
Let us observe the solution step by step.
Now, let us have a look at the slope-intercept form of a line.
Given: (x1, y1) = (2, 7) and m = 2 where 'm' denotes the slope of the given line.
Hence we can write the equation in slope-intercept form as given below.
(y − y1) = m (x − x1)
On substituting the given value of (x1, y1) = (2, 7) and m = 2, we get
(y − 7) = 2 (x − 2)
⇒ y - 7 = 2x - 4
On further simplifying the above equation we get,
y = 2x + 3
Hence, the slope-intercept form equation of the line that passes through (2, 7) and has a slope of 2 is y = 2x + 3.