Question about the point slope formula

  • Thread starter theb2
  • Start date
  • #1
1
3

Homework Statement


What is another form of point slope formula

Homework Equations


Y = mx+b

The Attempt at a Solution


Y - y2 = m(x - x2)
I’m not sure I’m trying to find B but I don’t know how
 

Answers and Replies

  • #2
FactChecker
Science Advisor
Gold Member
6,053
2,340
@theb2 , Your equation in the Solution section is the only point-slope form I know. It directly uses the given values of a point (x2, y2) and the slope, m. The equation in your "Relevant equations" is called the "slope-intercept" form. A guess you could rearrange the point-slope equation. Those would be cosmetic changes.

If you want to use a point and a slope to derive the slope-intercept form, then first rearrange your point-slope equation by isolating Y on the left by adding y2 to both sides. Then on the right side, separate the constants to give b and you already have the slope, m. Remember that x2 is a constant and a term with it becomes part of b.
 
Last edited:
  • #3
symbolipoint
Homework Helper
Education Advisor
Gold Member
6,115
1,161
Start with the formula for slope. One point is known and the other point is unknown. Multiply left and right sides by the binomial denominator, and that is the point-slope equation.
 
Last edited:
  • #4
34,687
6,394

Homework Statement


What is another form of point slope formula

Homework Equations


Y = mx+b
This, above, is the slope-intercept form of the equation of a line. There isn't another form, unless you use different names for the slope and y-intercept parameters.
theb2 said:

The Attempt at a Solution


Y - y2 = m(x - x2)
This is the point-slope form of the equation of a line. .
theb2 said:
I’m not sure I’m trying to find B but I don’t know how
You can find the y-intercept, b, by setting x to 0.
 
  • Like
Likes FactChecker
  • #6
symbolipoint
Homework Helper
Education Advisor
Gold Member
6,115
1,161
x/a + y/b = 1
Not sure just what you want here. Not sure if it is "Standard Form" or "General Form", but there's this form: Ax+By=C, a very common linear equation form. In your case you simply have A=1/a and B=1/b, and C=1.

You can solve for y in terms of x, and use whatever point you have given or know is on the line to write in point-slope form.
y/b=-x/a+1
y=-(b/a)x+b and slope is -(b/a). But this is still in slope-intercept form.

Let some point (xo, yo) be on this line. Your point slope equation is or can be
y-yo=-(b/a)(x-xo).
 
  • Like
Likes YoungPhysicist
  • #7
Not sure just what you want here. Not sure if it is "Standard Form" or "General Form", but there's this form: Ax+By=C, a very common linear equation form. In your case you simply have A=1/a and B=1/b, and C=1.

You can solve for y in terms of x, and use whatever point you have given or know is on the line to write in point-slope form.
y/b=-x/a+1
y=-(b/a)x+b and slope is -(b/a). But this is still in slope-intercept form.
Thanks. I am actually just viewing this thread and thought: OP needs another form of the formula, so I posted it.Since in the lesson I got from school, x/a +y/b =1 and y= mx+b are considered as different forms.
 
  • #8
symbolipoint
Homework Helper
Education Advisor
Gold Member
6,115
1,161
Thanks. I am actually just viewing this thread and thought: OP needs another form of the formula, so I posted it.Since in the lesson I got from school, x/a +y/b =1 and y= mx+b are considered as different forms.
Good. That's a start. Learn to understand, use, and internconvert among the different linear equation forms.
 
  • Like
Likes YoungPhysicist
  • #9
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,358
1,031
x/a + y/b = 1
This is the intercept - intercept form of a line, with x-intercept of a and y-intercept of b .
 
  • Like
Likes symbolipoint
  • #10
symbolipoint
Homework Helper
Education Advisor
Gold Member
6,115
1,161
This is the intercept - intercept form of a line, with x-intercept of a and y-intercept of b .
Neat! I never knew to know that as a basic form for a line. The other three forms have been more common. Now this one, two intercepts clearly shown in one equation.
 
  • Like
Likes YoungPhysicist
  • #11
Neat! I never knew to know that as a basic form for a line. The other three forms have been more common. Now this one, two intercepts clearly shown in one equation.
You can now say something at the “today I learned”:wink:
 

Related Threads on Question about the point slope formula

  • Last Post
Replies
2
Views
1K
Replies
5
Views
2K
Replies
2
Views
2K
Replies
12
Views
904
Replies
22
Views
4K
  • Last Post
Replies
3
Views
1K
Replies
2
Views
12K
Replies
14
Views
3K
Top