Aline passes through point (3, 7) and has a slope of . the equation of the line is . if point a(x, 5) lies on the line, the value of x is . nextreset

(a) y = 3/4*x + 19/4

(b) x = 1/3

Step-by-step explanation:

Assumption: line slope (m) is 3/4  

(a)

Line general formula is y = m*x + b. In this exercise, you knew a point which lies on the line and its slope. So, replacing in the formula and solving for b gives

7 = 3/4*3 + b

b = 7 - 9/4

b = 19/4

Then, the equation of the line is y = 3/4*x + 19/4

(b)

Replacing the point into the formula obtained previously and solving for x gives

5 = 3/4*x + 19/4

x = (5 - 19/4)*4/3

x = 1/3

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places