Question 1172310
Absolutely! Let's break down each part of the problem.

**a) Y = 2X - 3**

1.  **Standard Straight Line Formula:**
    * The typical standard straight-line formula is y = mx + b, where:
        * m is the slope (gradient) of the line.
        * b is the y-intercept (the value of y when x = 0).
    * In this case, y = 2x - 3, so:
        * m = 2
        * b = -3

2.  **Straight Line Graph:**
    * To draw the graph, you can:
        * Choose a few values of x within the given range (-3.5 to 5.5).
        * Calculate the corresponding y values.
        * Plot the points (x, y) on a coordinate plane.
        * Draw a straight line through the points.
    * Here's how to calculate a couple of points.
        * if x = 0, y = 2(0) - 3 = -3. (0, -3)
        * if x = 1, y = 2(1) - 3 = -1. (1, -1)

3.  **Steps in the Ratio of the Y Value of the Gradient:**
    * The gradient (slope) is 2. This means that for every 1 unit increase in x, y increases by 2 units.
    * The ratio of the change in y to the change in x is 2/1.

**b) 2Y = 8X - 1**

1.  **Standard Straight Line Formula:**
    * First, we need to rearrange the equation to the standard form (y = mx + b):
        * 2y = 8x - 1
        * y = 4x - 1/2
    * Now, we can identify:
        * m = 4
        * b = -1/2

2.  **Straight Line Graph:**
    * Similar to part a, choose x values within the range (-3.2 to 6.3), calculate y values, and plot the points.
    * Here are a few points.
        * if x = 0, y = 4(0) - 1/2 = -1/2 (0, -0.5)
        * if x = 1, y = 4(1) - 1/2 = 3.5 (1, 3.5)

3.  **Steps in the Ratio of the Y Value of the Gradient:**
    * The gradient (slope) is 4. This means that for every 1 unit increase in x, y increases by 4 units.
    * The ratio of the change in y to the change in x is 4/1.

**Gradient Comparison**

* The gradient of the first line (y = 2x - 3) is 2.
* The gradient of the second line (y = 4x - 1/2) is 4.
* The second line has a steeper slope than the first line.
* The second line's gradient is twice that of the first line. (4/2 = 2)