Question

the table. fill in the formula for each of the following forms of equations.
slope intercept form
point slope form
standard form
6.7 point slope form to slope intercept form
convert each equation from point slope form to slope intercept form

1. ( y - 4 = 2(x + 1) )
2. ( y + 5 = -\frac{3}{4}(x - 8) )

6.8 standard form to slope intercept form
convert each equation from standard form to slope intercept form

1. ( 4x + 2y = -6 )
2. ( 3x - 6y = 12 )

Explanation:

Problem 17: Convert \( y - 4 = 2(x + 1) \) to Slope - Intercept Form

Step 1: Distribute the slope

We use the distributive property \( a(b + c)=ab+ac \) to expand the right - hand side of the equation. Here, \( a = 2 \), \( b=x \) and \( c = 1 \).
\( y-4=2\times x+2\times1 \)
\( y - 4=2x + 2 \)

Step 2: Solve for \( y \)

We add 4 to both sides of the equation to isolate \( y \).
\( y-4 + 4=2x+2 + 4 \)
\( y=2x+6 \)

Problem 18: Convert \( y + 5=-\frac{3}{4}(x - 8) \) to Slope - Intercept Form

Step 1: Distribute the slope

Using the distributive property \( a(b - c)=ab - ac \) where \( a=-\frac{3}{4} \), \( b = x \) and \( c = 8 \).
\( y + 5=-\frac{3}{4}x-\frac{3}{4}\times(-8) \)
\( y + 5=-\frac{3}{4}x + 6 \)

Step 2: Solve for \( y \)

Subtract 5 from both sides of the equation.
\( y+5 - 5=-\frac{3}{4}x+6 - 5 \)
\( y=-\frac{3}{4}x + 1 \)

Problem 19: Convert \( 4x+2y=-6 \) to Slope - Intercept Form

Step 1: Isolate the \( y \) - term

Subtract \( 4x \) from both sides of the equation.
\( 2y=-4x - 6 \)

Step 2: Solve for \( y \)

Divide every term in the equation by 2.
\( y=\frac{-4x}{2}-\frac{6}{2} \)
\( y=-2x - 3 \)

Problem 20: Convert \( 3x-6y = 12 \) to Slope - Intercept Form

Answer:

s:

1. \( y = 2x+6 \)
2. \( y=-\frac{3}{4}x + 1 \)
3. \( y=-2x - 3 \)
4. \( y=\frac{1}{2}x-2 \)