Question about the point slope formula

[theb2]

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

 

[FactChecker]

@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.

 

[symbolipoint]

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.

 

[Mark44]

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.

The Attempt at a Solution

Y - y2 = m(x - x2)

This is the point-slope form of the equation of a line. .

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.

 

[YoungPhysicist]

x/a + y/b = 1

 

[symbolipoint]

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 (x_o, y_o) be on this line. Your point slope equation is or can be
y-y_o=-(b/a)(x-x_o).

 

[YoungPhysicist]

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.

 

[symbolipoint]

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.

 

[SammyS]

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]

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]

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”