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Math  /  Algebra

Questionn=−22,(−3,−1)\boldsymbol{n} = -\frac{2}{2}, (-3, -1)
\text{GENERAL form}

Studdy Solution

STEP 1

1. The slope of the line is m=−23 m = -\frac{2}{3} .
2. The line passes through the point (−3,−1) (-3, -1) .
3. We need to find the equation of the line in general form Ax+By+C=0 Ax + By + C = 0 .

STEP 2

1. Use the point-slope form of the line equation.
2. Convert the point-slope form to slope-intercept form.
3. Convert the slope-intercept form to general form.

STEP 3

Start with the point-slope form of the line equation, which is:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
where m=−23 m = -\frac{2}{3} and the point (x1,y1)=(−3,−1) (x_1, y_1) = (-3, -1) .
y−(−1)=−23(x−(−3)) y - (-1) = -\frac{2}{3}(x - (-3))

STEP 4

Simplify the point-slope equation to slope-intercept form y=mx+b y = mx + b :
y+1=−23(x+3) y + 1 = -\frac{2}{3}(x + 3)
Distribute the slope on the right side:
y+1=−23x−2 y + 1 = -\frac{2}{3}x - 2
Subtract 1 from both sides to solve for y y :
y=−23x−3 y = -\frac{2}{3}x - 3

STEP 5

Convert the slope-intercept form to the general form Ax+By+C=0 Ax + By + C = 0 :
Start with the equation:
y=−23x−3 y = -\frac{2}{3}x - 3
Multiply all terms by 3 to eliminate the fraction:
3y=−2x−9 3y = -2x - 9
Rearrange to get all terms on one side:
2x+3y+9=0 2x + 3y + 9 = 0
This is the general form of the line.
The general form of the line is 2x+3y+9=0 \boxed{2x + 3y + 9 = 0} .

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