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Question 1172310: In a design of a highway, a survey for the hill side shows that it is in the following
Formulae :
a) Y= 2X-3 ; Y given the value of X BETWEEN -3.5 TO + 5.5 . State the typical standard straight line formula; Draw Straight Line GRAPH for the two formula and Find the steps in the ratio the Y value of the Gradient.
b) 2Y= 8X-1 ; given the value of X BETWEEN -3.2 TO + 6.3 . State the typical standard straight line formula; Draw Straight Line GRAPH for the formula and Find the steps in the ratio the Y value of the Gradient.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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)
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