Question

(b) which of the following points (x, y)correctly represent the given information that rent in the 6
a (1250,6)
b (6,1250)
c (60,1250)
d (60,6)
(c) which equation is the correct point - slope form of the linear equation that models the rent?
a y + 1250 = 60(x + 6)
b y - 6 = 60(x - 1250)
c y - 1250 = 60(x - 6)
d y - 1250 = 6(x - 60)

Explanation:

Part (b)

Step1: Understand the context

Assuming \( x \) represents time (e.g., months) and \( y \) represents rent. We need to match the point \((x,y)\) with the given options.

Step2: Analyze the options

• Option A: \((1250, 6)\) – Unlikely, as rent (y) is usually larger than time (x) in such contexts.
• Option B: \((6, 1250)\) – If \( x = 6 \) (time) and \( y = 1250 \) (rent), this makes sense.
• Option C: \((60, 1250)\) – 60 as time might not align with typical rent scenarios here.
• Option D: \((60, 6)\) – Rent of 6 is unrealistic.

Step1: Recall point - slope form

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \), where \((x_1,y_1)\) is a point on the line and \( m \) is the slope.

Step2: Identify the point and slope

From part (b), we have the point \((6,1250)\) (so \( x_1 = 6 \), \( y_1=1250 \)). Let's assume the slope \( m = 60 \) (from the context of the problem, maybe rate of change of rent with respect to time).
Substituting into the point - slope form: \( y - 1250=60(x - 6) \)

• Option A: \( y + 1250=- 60(x + 6) \) – Wrong sign and point.
• Option B: \( y - 6=60(x - 1250) \) – Wrong point.
• Option C: \( y - 1250 = 60(x - 6) \) – Correct as per point - slope form.
• Option D: \( y - 1250=6(x - 60) \) – Wrong slope and point.

Answer:

B. (6,1250)

Part (c)