# Question about the point slope formula

• theb2
In summary, the form of an equation of a line that uses two points (x1, y1), (x2, y2) is the slope-intercept form.

## Homework Statement

What is another form of point slope formula

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

@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.

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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.

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theb2 said:

## 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.

FactChecker
x/a + y/b = 1

FactChecker
Young physicist said:
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).

YoungPhysicist
symbolipoint said:
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.

Young physicist said:
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.

YoungPhysicist
Young physicist said:
x/a + y/b = 1
This is the intercept - intercept form of a line, with x-intercept of a and y-intercept of b .

symbolipoint
SammyS said:
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.

YoungPhysicist
symbolipoint said:
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”