Respuesta :

Answer:

y = [tex]\frac{3}{2}[/tex] x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{3}{2}[/tex] , thus

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 12 + c ⇒ c = 4 - 12 = - 8

y = [tex]\frac{3}{2}[/tex] x - 8 ← equation of line

akposevictor

The equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] (point-slope form) or

[tex]y = \frac{3}{2}x - 8[/tex] (slope-intercept form).

Given:

a point on a line: (8, 4)

slope of the line: 3/2

The equation of the line can be written in either point-slope form or slope-intercept form.

First, let's write the equation in point-slope form since we know one of the points and the slope.

  • Point-slope equation takes the form: y - b = m(x - a)

Where,

  • (8, 4) = (a, b), and
  • m = 3/2

  • Substitute

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] =>> point-slope form.

  • Also, we can rewrite in slope-intercept form as follows:

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex]

  • Open bracket

[tex]y - 4 = \frac{3}{2}x - 12[/tex]

  • Add 4 to both sides

[tex]y - 4 + 4 = \frac{3}{2}x - 12 + 4\\\\y = \frac{3}{2}x - 8[/tex](slope-intercept form)

Therefore, the equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

[tex]y - 4 = \frac{3}{2} (x - 8)[/tex] (point-slope form) or

[tex]y = \frac{3}{2}x - 8[/tex] (slope-intercept form).

Learn more here:

https://brainly.com/question/13967935

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