When you use this: (0,2);m=4/5
and write it in point-slope form, does it become (y-2)=4/5(x-0)?
yes
Is(y-2)=4/5(x-0) the most simplified answer? Can it be changed into(y-2)=4/5x?
no, you would expand and simplify ...
y - 2 = (4/5)x , times 5
5y - 10 = 4x
in general form: 4x - 5y + 10 = 0
slope-y intercept form: y = (4/5)x + 2
First question: no, the zero can be dropped
Second question: yes it can be changed into (y-2) = (4/5)*x and it can be also be re-written as
y = (4/5)*x + 2 [slope intercept form]
Hope that helps
Yes, when you have a point-slope equation in the form of (0,2); m=4/5, you can indeed write it in point-slope form as (y-2) = (4/5)(x-0).
To understand how to get this equation, let's break it down step by step:
1. Starting with the given information, the point-slope form of a linear equation is written as (y - y₁) = m(x - x₁), where (x₁, y₁) represents a point on the line and m represents the slope of the line.
2. In this case, the given information is (0,2) as the point on the line and m = 4/5 as the slope.
3. Substituting these values into the point-slope form equation, we get (y - 2) = (4/5)(x - 0). Since the x-coordinate of the given point is 0, we can simplify it to (y - 2) = (4/5)x.
4. The equation (y - 2) = (4/5)x represents a line with a slope of 4/5 passing through the point (0,2). This is the final equation in point-slope form.
Note: If you need to convert the equation to another form, such as slope-intercept form (y = mx + b), you can simplify it further by distributing the (4/5) coefficient and rearranging the terms.