📌 Fixed cost = $30 (base monthly charge)
Variable cost = $0.10 per text = 0.10t
Total: C = 30 + 0.10t

💡 This is a linear equation in slope-intercept form: y = mx + b where m = 0.10 and b = 30.

📌 Negative slope = line goes DOWN from left to right (↘).
Positive slope = line goes UP from left to right (↗).
Graph B has negative slope.

Function notation f(3) means *"evaluate the function at x = 3"*. Replace every x in the expression with 3, then simplify using order of operations:

f(3) = 2(3) + 5 = 6 + 5 = $11.

Real-world reading: at 3 GB, the bill is the $5 flat fee plus $2 × 3 = $6 of data charges = $11 total.

Why the distractors fail: each one applies the wrong operation order or invents extra terms. Always do multiplication (2 × 3) BEFORE addition when evaluating a linear function.

📌 Common difference d = 7 − 3 = 4
a_n = a_1 + (n−1)d = 3 + (10−1)(4) = 3 + 36 = 39

📌 The lines are parallel (same slope, different y-intercepts).
Parallel lines NEVER intersect → NO solution.

Systems with no solution are called 'inconsistent.'

📌 Points trend downward from left to right → negative correlation.
As x increases, y decreases.

📌 Points trend upward from left to right → positive correlation.
As hours studied increases, test score increases.
The trend line slopes upward → positive relationship.

📌 The solution is where the lines intersect = (1, 2).
Verify: y = x + 1 → 2 = 1 + 1 ✓
y = −x + 3 → 2 = −1 + 3 ✓

📌 y = 2x + 1:
• Slope = 2 (positive → goes UP)
• y-intercept = 1 (crosses y-axis above origin)
Graph A shows positive slope with y-intercept above origin.