Respuesta :
Answer:
The initial value of the graph is 2. Third option is correct.
Step-by-step explanation:
It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
The line is passing through the points (0,2) and (7,5).
The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.
Slope of line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]
The equation of line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept. So the equation of given line is
[tex]y=\frac{3}{7}x+2[/tex]
At initial condition the value of x is 0. So, put x=0.
[tex]y=\frac{3}{7}(0)+2=2[/tex]
Therefore the initial value of the graph is 2. Option 3 is correct.
Answer:
Option 3 rd is correct
Initial value = 2
Step-by-step explanation:
A equation of line is given by:
[tex]y =mx+b[/tex] ....[1]
where
m is the slope of the line and b is the y-intercept or the initial value
As per the statement:
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
It is also given that:
A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)
Calculate slope:
using formula:
[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given ordered pairs we have;
[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]
y-intercept states that the graph which cut y-axis.
Substitute x =0 and solve for x:
we have given with the ordered pair (0, 2)
⇒y-intercept(b) = 2
Substitute the given values of m and b in [1]
[tex]y = \frac{3}{7}x+2[/tex]
The equation of straight line joins the ordered pair (0, 2) with the ordered pair (7, 5) is:
[tex]y = \frac{3}{7}x+2[/tex]
The initial value of the function represented by the given graph as shown below is: 2
