Write an equation in point-slope form for the line through the given point with the given slope m = 6 and point (8, 3).

Solution:

The slope of a curve at a particular point is given by the ratio of rise over run at that particular point. It has many applications in the field of coordinate geometry. 

Given: Point (8, 3) and Slope m = 6

Now, we use the point-slope formula,

y - y₁ = m (x - x₁) 

Here, x₁ = 8 and y₁ = 3.

Hence, substituting the values in the above equation, we get

y - 3 = 6 (x - 8)

⇒ y - 3 = 6x - 48

⇒ 6x - y = 48 - 3

⇒ y = 6x - 45.

Hence, the equation in point-slope form for the line through the given point with the given slope m = 6 and point (8, 3) is y = 6x - 45.

Write an equation in point-slope form for the line through the given point with the given slope m = 6 and point (8, 3).

Summary:

The equation in point-slope form for the line through the given point with the given slope m = 6 and point (8, 3) is y = 6x - 45.