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If the x- intercept is 2 and the y- intercept is -5 and the slope is 1/3. Write in equation in slope intercept form and standard form.

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Answer:

  • The equation in slope-intercept form is

[tex]y=\frac{5}{2}x-5[/tex]

  • The equation in the standard form will be:

[tex]\frac{5}{2}x-y=5[/tex]

Step-by-step explanation:

  • The x-intercept is obtained when we set the value y=0

As the x-intercept is 2, therefore the point representing

the x-intercept will be: (2, 0)

  • The y-intercept is obtained when we set the value x=0

As the y-intercept is -5, therefore the point representing

the y-intercept will be: (0, -5)

So we get the two points

(2, 0)

(0, -5)

Finding the slope between (2, 0) and (0, -5)

[tex]\left(x_1,\:y_1\right)=\left(2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)[/tex]

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-5-0}{0-2}[/tex]

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

Using the point-slope form of the line equation

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

Here m is the slope

substituting the values m = 5/2 and the point (2, 0)

[tex]y-0=\frac{5}{2}\left(x-2\right)[/tex]

so writing the equation in slope-intercept form

As we know that the slope-intercept form is

[tex]y=mx+b[/tex]

here

  • m = gradient or slop
  • b = y-intercept

so

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

[tex]y=\frac{5}{2}x-5[/tex]

Hence, the equation in slope-intercept form is

[tex]y=\frac{5}{2}x-5[/tex]

Writing the equation in the standard form form

As we know that the equation in the standard form is

[tex]Ax+By=C[/tex]

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

[tex]y=\frac{5}{2}x-5[/tex]

so the equation in the standard form will be:

[tex]\frac{5}{2}x-y=5[/tex]

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