Answer:
k = 6.5
Step-by-step explanation:
The question relates to the association of the association of the equation of a graph point(s) on the graph
The given equation of the graph, is y = 2·x + c
The value of 'c' is a constant
We note that the value of 'c' can be found when x = 0, as follows;
y = 2·x + c = 2 × 0 + c = c
∴ When x = 0, y = c
From the graph, when x = 0 we have the y-intercept, the point the graph crosses the y-axis, which is the point y = -3
Therefore;
When x = 0, y = -3 = c
∴ c = -3
The equation of the graph becomes, y = 2·x + (-3) = 2·x - 3
y = 2·x - 3
The other given point on the graph is the point (k, 10)
The value k is the x-value when y = 10
Substituting y = 10 in the equation for the graph gives the x-value at the point y = 10 as follows;
10 = 2·x - 3
2·x = 13
x = 13/2 = 6.5
x = 6.5 (when y = 10)
Therefore the point (k, 10) = (6.5, 10)
By comparing the two equal coordinates, we have;
k = 6.5.
