Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2?

Solution:

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.

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.

Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2?

Summary:

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.