standard fourm of the equasion that is parallell to 2x-5y=-15and goes through (-5,4)

Question

write the standard fourm of the equasion that is parallell to 2x-5y=-15and goes through (-5,4)

 

Answer 1

Hello Alicia,

 

The following is my breakdown of this problem.

 

Note: Standard format is Ax + By = C where A,B, & C can not be in fraction or decimal format

 

English: Find slope of given equation 2x - 5y = -15 by solving for y

 

English: subtract 2x from both sides

Math: -5y = -2x - 15

 

English: Divide all terms by -5

Math: y = 2/5x + 3

 

English: Identify Slope

Math: m = 2/5 (So we know that the new equation will have a slope of 2/5 but a different y-intercept which is the definition of parallel lines)

 

English: write format for slope-intercept and substitute the x & y from the given point and the slope to find the y-intercept ( b )

Math: y = mx  + b point (-5,4) where x = -5 and y = 4

         4 = (2/5)(-5) + b

         4 = -2 + b

         6 = b

 

English: Rewrite equation in y = mx + b format
Math:  y = 2/5x + 6

 

English: Convert Equation of y = 2/5x + 6 into Standard Format Ax + By = C

             Subtract 2/5x from both sides

Math: -2/5x + y = 6

 

English: Multiply every term by -5 (This is to get rid of the fraction)

Math:  2x - 5y = -30

 

English: Write Answer

 

The standard format of the equation that is parallel to 2x - 5y = -15 is 2x - 5y = -30

 

I hope that Helps!

 

 

Answer 2

Rewrite the original equation in y=mx+b form.

 

-5y=-2x-15

 

y=(2/5)x+3

 

Substitute the values into the equation to find the y-intercept.

 

4 = (2/5)(-5)+b

4 = -2+b

6 = b

 

Your equation is

 

y = (2/5)x+6