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The​ point-slope form of the equation of a nonvertical line with slope, m, that passes through the point (x1,y1) is...?

a. Ax+By=c

b. y-y1=m(x-x1)

c. y1=mx1+b

d. Ax1+by1=C

e. y=mx+b

f. y1-y=m(x-x1)

Please explain why, if you can. Thanks! :)

Respuesta :

sqdancefan

Answer:

  b. y-y1 = m(x-x1)

Step-by-step explanation:

It's a matter of definition. There are perhaps a dozen useful forms of equations for a line. Each has its own name (and use). Here are some of them.

  • slope-intercept form: y = mx + b
  • point-slope form: y -y1 = m(x -x1)
  • two-point form: y = (y2-y1)/(x2-x1)(x -x1) +y1
  • intercept form: x/a +y/b = 1
  • standard form: ax +by = c
  • general form: ax +by +c = 0

Adding y1 to the point-slope form puts it in an alternate form that is useful for getting to slope-intercept form faster: y = m(x -x1) +y1. I use this when asked to write the equation of a line with given slope through a point, with the result in slope-intercept form.

The equation of the line, in point-slope form, is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

Option b.

-----------------------------------------

The equation of a line, in point-slope form, is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

In which

  • m is the slope.
  • The point is [tex](x_1,y_1)[/tex].
  • Nonvertical line means that [tex]m \neq 0[/tex]
  • Thus, the correct option is given by option b.

A similar problem is given at https://brainly.com/question/24144915

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