SOLUTION: Variables x and y are such that when lg(2y+1) is plotted against x^2, a straight line graph passing through the points (1,1) and (2,5) is obtained. a) Find y in terms of x. b) f

Question 1196470: Variables x and y are such that when lg(2y+1) is plotted against x^2, a straight line graph passing through the points (1,1) and (2,5) is obtained.
a) Find y in terms of x.
b) find the value of y when x = √3/2.
c) Find the value of x when y = 2.
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
**1. Determine the Equation of the Line**
* **Given Points:** (1, 1) and (2, 5)
* Where (x², lg(2y+1)) are the coordinates
* **Calculate Slope (m):**
* m = (y2 - y1) / (x2² - x1²)
* m = (5 - 1) / (2² - 1²) = 4 / 3
* **Calculate y-intercept (c):**
* Using point (1, 1):
* 1 = (4/3) * 1² + c
* c = 1 - 4/3 = -1/3
* **Equation of the line:**
* lg(2y+1) = (4/3)x² - 1/3
**2. Find y in terms of x (Part a)**
* lg(2y+1) = (4/3)x² - 1/3
* 2y+1 = 10^[(4/3)x² - 1/3]
* 2y = 10^[(4/3)x² - 1/3] - 1
* y = [10^[(4/3)x² - 1/3] - 1] / 2
**3. Find the value of y when x = √3/2 (Part b)**
* y = [10^[(4/3)*(√3/2)² - 1/3] - 1] / 2
* y = [10^[(4/3)*(3/4) - 1/3] - 1] / 2
* y = [10^(1 - 1/3) - 1] / 2
* y = [10^(2/3) - 1] / 2
* y ≈ 1.8208
**4. Find the value of x when y = 2 (Part c)**
* lg(2*2 + 1) = (4/3)x² - 1/3
* lg(5) = (4/3)x² - 1/3
* (4/3)x² = lg(5) + 1/3
* x² = 3/4 * (lg(5) + 1/3)
* x = ± √[3/4 * (lg(5) + 1/3)]
* x ≈ ± 0.8799
**Therefore:**
* **a) y = [10^[(4/3)x² - 1/3] - 1] / 2**
* **b) y ≈ 1.8208 when x = √3/2**
* **c) x ≈ ± 0.8799 when y = 2**

RELATED QUESTIONS
Variables x and y are such that, when e^y is plotted against x^2, a straight line graph... (answered by CPhill)

The variables x and y satisfy the equation y=A(b^-x), where A and b are constants. The... (answered by tommyt3rd)

The variable x and y are such that the graph of log10y aganist x is a straight line... (answered by josgarithmetic)

The variable x and y are such that graph of log10y aganist x is a straight line passing... (answered by ikleyn)

A straight line that is parallel to line -x+2y+2=0 and passes through the points (a,1)... (answered by ewatrrr)

lg(x-1)=2 (answered by mananth)

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 2 8 6 11 13... (answered by ikleyn)

please help with homework 1) is the relation xy=5 a function within the domain(-5,-1)... (answered by stanbon)