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Determine the intercepts of the line.
Do not round your answers.

−3x − 4 = −5y − 8

1. y-intercept: ( , )
2. x-intercept: ( , )

Respuesta :

Simplify the expression

[tex]\\ \sf\longmapsto -3x-4=-5y-8[/tex]

[tex]\\ \sf\longmapsto 3x+4=5y+8[/tex]

[tex]\\ \sf\longmapsto 3x-5y=4[/tex]

[tex]\\ \sf\longmapsto 3x=5y+4[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{5y+4}{3}[/tex]

X intercept:-

Now

  • Take y =0

[tex]\\ \sf\longmapsto x=\dfrac{5(0)+4}{3}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{4}{3}[/tex]

Hence.

[tex]\\ \sf\longmapsto x=\left(\dfrac{4}{3},0\right)[/tex]

Y intercept

  • Take x=0

[tex]\\ \sf\longmapsto y=\dfrac{3x-4}{5}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{3(0)-4}{5}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{-4}{5}[/tex]

Hence

[tex]\\ \sf\longmapsto y=\left(0,\dfrac{-4}{5}\right)[/tex]

Ver imagen Аноним
Lanuel

The intercepts of the given line is equal to (0, [tex]\frac{-4}{5}[/tex]) and ([tex]\frac{4}{3}[/tex], 0).

Given the following data:

  • [tex]-3x - 4 = -5y - 8[/tex]

To determine the intercepts of the given line:

How to calculate the intercepts of a line.

First of all, we would simplify the given equation of line as follows:

[tex]-3x - 4 = -5y - 8\\\\5y=3x+4-8\\\\5y=3x-4\\\\y=\frac{3x}{5} -\frac{4}{5}[/tex]

When x = 0, y-intercept equals:

[tex]y= \frac{3(0)-4}{5} \\\\y= \frac{0-4}{5} \\\\y= \frac{-4}{5}[/tex]

y-intercept = (0, [tex]\frac{-4}{5}[/tex])

When y = 0, x-intercept equals:

[tex]x= \frac{5y+4}{3} \\\\x= \frac{0+4}{3} \\\\x= \frac{4}{3}[/tex]

x-intercept = ([tex]\frac{4}{3}[/tex], 0)

Read more on intercept here: https://brainly.com/question/3493733

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