Answer: the value of 'a' is 0, and the value of 'b' is approximately 0.645.
Explanation:
To find the values of 'a' and 'b' in the equation of the line representing the relationship between pounds and euros, we can use the given information that £1 is equal to 1.55 euros.
In the equation of a straight line, y = mx + c, 'm' represents the slope of the line and 'c' represents the y-intercept.
Given that (0, a) is on the line, the x-coordinate is 0, and the y-coordinate is 'a'. Similarly, given that (1, b) is on the line, the x-coordinate is 1, and the y-coordinate is 'b'.
The slope, 'm', can be calculated as the change in y divided by the change in x:
m = (b - a) / (1 - 0)
m = (b - a) / 1
m = b - a
We know that £1 is equal to 1.55 euros. Therefore, when x = 1 (1 pound), y (in euros) would be 1 * 1.55 = 1.55.
This gives us the equation:
1 = (b - a) * 1.55
Simplifying the equation, we get:
1 = 1.55b - 1.55a
From here, we can equate the coefficients of 'a' and 'b' on both sides of the equation:
-1.55a = 0
a = 0
1.55b = 1
b = 1 / 1.55
b ≈ 0.645