Question

period:
wednesday
solve for x. how many solutions?
$-3 + x - 4 = 2 + 3x + 5 - 2x$
function a is given by the equation $y = 3x + 10$. function b shown.
function b

x	y
1	10
2	13
3	16
4	19

fill in the blank
function a has a y - intercept.
function b has a slope.
thursday
maya is asked to solve the equation $2(3x + 6) = 3(x - 10)$.

given	$2(3x + 6) = 3(x - 10)$
step 1	$6x + 12 = 3(x - 10)$
step 2	$6x + 12 = 3x + 30$
step 3	$3x + 12 = 30$
step 4	$3x = 18$
step 5	$x = 6$

complete the sentance.
maya made a mistake between steps &
solve to get the correct answer.

Explanation:

Wednesday - Solve for \( x \), How many solutions?

Step 1: Simplify both sides

Simplify left side: \( -3 + x - 4 = x - 7 \)
Simplify right side: \( 2 + 3x + 5 - 2x = x + 7 \)
Equation becomes: \( x - 7 = x + 7 \)

Step 2: Subtract \( x \) from both sides

\( x - x - 7 = x - x + 7 \)
Simplifies to: \( -7 = 7 \)

• For Function A, the equation \( y = 3x + 10 \) is in slope - intercept form (\( y=mx + b \)), so the y - intercept is 10.
• For Function B, using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1}\) with two points \((1,10)\) and \((2,13)\), the slope is 3.

Given equation: \( 2(3x + 6)=3(x - 10) \)

Step 1: Distribute left side

\( 2(3x)+2(6)=6x + 12 \) (correct)

Step 2: Distribute right side

\( 3(x)-3(10)=3x - 30 \), but Maya wrote \( 3x + 30 \). So the mistake is in Step 2 (distributing the - 10 with 3: \( 3\times(- 10)=-30 \), not + 30).

Step 3: Let's correct and solve

Starting from correct Step 2: \( 6x + 12 = 3x - 30 \)
Subtract \( 3x \): \( 3x + 12=-30 \)
Subtract 12: \( 3x=-42 \)
Divide by 3: \( x = - 14 \)

Answer:

No solution (the equation is a contradiction).

Wednesday - Function A and Function B

Function A's y - intercept

Function A: \( y = 3x + 10 \). The slope - intercept form is \( y = mx + b \), where \( b \) is the y - intercept. So for \( y = 3x+10 \), the y - intercept \( b = 10 \).

Function B's slope

For a linear function, the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points \((1,10)\) and \((2,13)\) from Function B's table:
\( m=\frac{13 - 10}{2 - 1}=\frac{3}{1}=3 \)