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Which equation represents a line that passes through (–2, 4) and has a slope of StartFraction 2 Over 5 EndFraction.? y – 4 = (x + 2) y + 4 =(x – 2) y + 2 = (x – 4) y – 2 =(x +4)

Respuesta :

carlosego

For this case we have that by definition, the point-slope equation of a line is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes

m: It is the slope of the line

According to the data we have to:

[tex](x_ {0}, y_ {0}): (-2,4)\\m = \frac {2} {5}[/tex]

Substituting:

[tex]y-4 = \frac {2} {5} (x - (- 2))\\y-4 = \frac {2} {5} (x + 2)[/tex]

Finally, the equation of the line is:

[tex]y-4 = \frac {2} {5} (x + 2)[/tex]

ANswer:

[tex]y-4 = \frac {2} {5} (x + 2)[/tex]

akposevictor

The equation representing the line is: [tex]\mathbf{y - 4 = \frac{2}{5}(x + 2)}[/tex]

Recall:

  • Equation of a line can be written in point-slope form if we know the slope value (m) and a point (a, b) that the line passes through.

Given:

  • A point on the line: (–2, 4)

  • Slope of the line: [tex]\frac{2}{5}[/tex]

  • Thus:

The equation in point-slope form of any line is:

[tex]y - b = m(x - a)[/tex]

  • Where,

a = -2

b = 4

[tex]m = \frac{2}{5}[/tex]

  • Substitute the values into the point-slope equation:

[tex]y - 4 = \frac{2}{5}(x - (-2))\\\\y - 4 = \frac{2}{5}(x + 2)[/tex]

Therefore, the equation that represents the line with a slope of 2/5 and passes through the point (-2, 4) is:

[tex]y - 4 = \frac{2}{5}(x + 2)[/tex]

Learn more here:

https://brainly.com/question/16720682

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