The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points =
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope =
slope =
We know slope =4
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Answer:
(a) The data set is a function, since for each input value {3,4,6,11} there is a single output value {5,7,11,21}
(B) A function is a mathematical relationship that associates one or more inputs with a single output value. So that the data set is not a function, there should be - for one or more values of the input - more than one output.
for example, if for the input value {3} there were two outputs {5, -5} then, the data set would not be a function.
The frelation is not a function because:
When x = 1, y = +1 and y = -1.
(c) The set of data provided can be represented by the equation of a line of the form y = mx + b
The slope is:
m = 2
b = 5 - 2*3
b = -1
Then, the function is:
y = 2x-1
You can substitute any of the points shown in the equation and check that equality is satisfied, for example:
(11 , 21)
y = 2 (11) -1
y = 22-1
y = 21. The equation is satisfied. The same goes for the rest of the values.