Respuesta :

amysun2025

Answer:

[tex]y-2=3(x-4)[/tex]

Step-by-step explanation:

Pre-Solving

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

  • Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
  • Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well.
  • Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Solving

Substitute 3 as m in [tex]y-y_1=m(x-x_1)[/tex].

[tex]y-y_1=3(x-x_1)[/tex]

Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].

[tex]y-2=3(x-4)[/tex]

Topic: parallel and perpendicular lines

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