Is it possible to use these points: (4,-2),(9,-8)
and write an equation in slope intercept form, without first writing an equation in point-slope form, and then rewriting it to slope-intercept form?
sure, first find the slope
slope = (-8+2)/(9-4) = -6/5
then the equation is y = (-6/5)x + b
sub in (4,-2) , or the other point
-2 = (-6/5)(4) + b
I would now multiply by 5 (since I try to avoid fractions as much as possible)
-10 = -24 + 5b
b = 14/5
so y = (-6/5)x + 14/5
No, you have to first use
y - y1 = m(x - x1) [point slope form]
and then rewrite in the form
y = mx + c [slope intercept form]
When you are given 2 points you have to find the slope first
[m = (y2 - y1)/(x2 - x1)]
then sub in the slope with either of the points in the equation in point slope form.
Hope that helps.
I'll correct myself, yes you can I didn't think of the above method by Reiny.
I never used that way before :)
It's quite useful though.
Sorry for my error
why do you have to sub in (4,-2)? why can't you use 9,-8)?
As I said, you can use either point.
I usually use the point that has the "nicer" numbers. Either point will give you the same value of b
A good idea is to then use the other point to see if the equation works.
Yes, it is possible to write an equation in slope-intercept form using the given points (4,-2) and (9,-8) without first writing an equation in point-slope form.
To write an equation in slope-intercept form (y = mx + b), we need to find the values of slope (m) and y-intercept (b).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the coordinates (4,-2) as (x1, y1) and (9,-8) as (x2, y2):
m = (-8 - (-2)) / (9 - 4)
m = (-8 + 2) / (9 - 4)
m = -6 / 5
Now that we have the slope (m = -6/5), we need to find the y-intercept (b).
To find the y-intercept (b), we can use the formula:
b = y - mx
We can choose one of the given points to substitute for x and y. Let's use the point (4,-2):
b = -2 - (-6/5) * 4
b = -2 + 24/5
b = -2 + 4.8
b = 2.8
Now we have the slope (m = -6/5) and the y-intercept (b = 2.8). We can plug these values into the slope-intercept form equation:
y = (-6/5)x + 2.8
So, the equation in slope-intercept form using the given points is y = (-6/5)x + 2.8.