Question

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Answer 1

Answer:

Rate of change: $m = 5$

The initial value is 20

The equation: $y = 5x + 20$

Step-by-step explanation:

Given

The attached table

Solving (a): The rate of change (m)

This is calculated as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$(x_1,y_1) = (2,30)$

$(x_2,y_2) = (3,35)$

So:

$m = \frac{35- 30}{3- 2}$

$m = \frac{5}{1}$

$m = 5$

Solving (b): The initial value

Here, we make use of point (0, y) to calculate the initial value:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (0,y)$

$(x_2,y_2) = (3,35)$

$m = 5$

So:

$5 = \frac{35 - y}{3 - 0}$

$5 = \frac{35 - y}{3}$

Multiply both sides by 3

$3 * 5 = \frac{35 - y}{3}* 3$

$15 = 35 - y$

$y = 35 - 15$

$y = 20$

Solving (c): The equation

This is calculated using:

$y = m(x - x_1) + y_1$

Where:

$(x_1,y_1) = (2,30)$

$m = 5$

So, we have:

$y = 5(x - 2) + 30$

$y = 5x - 10 + 30$

$y = 5x + 20$