How to find x and y intercepts for the equation 2x+3y-15=0?

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

The x-intercept has a y-value of 0 and the y-intercept has an x-value of 0.  Therefore, you can find the x and y intercepts by substituting 0 in for each variable one at a time.

x-intercept:

2x + 3(0) - 15 = 0

2x - 15 = 0

2x = 15

x = 7.5

The x-intercept is (7.5, 0).

 

y-intercept:

2(0) + 3y - 15 = 0

3y - 15 = 0

3y = 15

y = 5

The y-intercept is (0, 5).

 

You can check this answer by graphing the line.

Rewrite the equation as y = (-2x + 15) / 3

The line intersects the x-axis at 7.5 and the y-axis at 5.

 

 

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation of a straight line in intercept-intercept form is x/a+y/b = 1 where a is the x-intercept and b is the y-intercept.

Convert the standard form of the equation of the line into the intercept-intercept form.

2x+3y-15=0

Add 15 to both the sides

2x+3y= 15

Divide both sides by 15

`(2x)/15 + (3y)/15 = 1`

`x/(15/2) + y/(15/3) = 1`

`x/7.5 + y/5 = 1`

The x-intercept of the line is 7.5 and the y-intercept is 5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine x axis intercept of the given line, we'll have to set y = 0.

2x + 3*0 - 15 = 0

2x - 15 = 0

x = 15/2

The x axis intercepting point is (15/2 ; 0).

To determine y axis intercept of the given line, we'll have to set x = 0.

2*0 + 3y - 15 = 0

3y - 15 = 0

3y = 15

y = 15/3

y = 5

The y axis intercepting point is (0 ; 5).

Therefore, the x and y axis intercepts are: (15/2 ; 0) and (0 ; 5).

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