SOLUTION: Write the equation of the line in standard form with y-intercept 3 and a slope of -2/3.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Write the equation of the line in standard form with y-intercept 3 and a slope of -2/3.       Log On


   

Question 1207294: Write the equation of the line in standard form with y-intercept 3 and a slope of -2/3.
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line in standard form
ax%2Bby=c

given:
y-intercept 3 => point (0,3)
a slope of m=-2%2F3

using point slope form we have

y-y%5B1%5D=m%28x-x%5B1%5D%29....substitute given values
y-3=-%282%2F3%29%28x-0%29
y-3=-%282%2F3%29x
y=-%282%2F3%29x%2B3...both sides multiply by 3
3y=-2x%2B9
2x%2B3y=9 => your equation

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%282%2F3%29x%2B3%29+


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Slope-intercept form is y+=+mx%2Bb
m = slope = -2/3
b = y intercept = 3

y+=+mx%2Bb will update to y+=+expr%28-2%2F3%29x%2B3

Multiply both sides by 3 to clear out the denominator.
Then add 2x to both sides so the variable terms are on one side, while the constant is on the other side.

y+=+expr%28-2%2F3%29x%2B3

3y+=+3%28expr%28-2%2F3%29x%2B3%29

3y+=+-2x%2B9

2x%2B3y+=+9 is the equation in standard form Ax+By = C