Find the equation of the line that has an x intercept at x = -4 and y intercept at y = 5

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We are given that the x intercept of the line is at x = -4 and the y intercept is at y = 5.

Now a standard form of the equation of a line with x and y intercepts is (x/a) + (y/b) = 1, where a and b are the x and y intercepts respectively.

Using this and substituting the values -4 and 5, we get:

x/-4 + y/5 = 1

Multiplying all the terms with 20

=> 5x - 4y = 20

=> 5x - 4y - 20 =0

Therefore the required equation is 5x - 4y - 20 = 0.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

The line has x intercept x = -4   and y intercept y= 5

Then the line passes throught the points:

A( -4, 0) and B( 0, 5)

now we will use the slope formula to determine the equation of the line:

y- y1 = m (x- x1)

Where (x1, y1) is any point of the line , we will use the point A(-4, 0)

==> y- 0 = m ( x + 4)

==> y = m ( x + 4)

Now we will calculate the slope m:

m = ( yB- yA)/ ( xB - xA)

    = ( 5-0) / ( 0 + 4)

     = 5/4

Then the slope m = 5/4

let us substitute in the equation:

y = m ( x+ 4)

==> y= (5/4) ( x + 4)

==> y= (5/4)x + 5

Multiply by 4:

==> 4y = 5x + 20

==> 4y - 5x - 20 = 0

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