Respuesta :
Answer:
[tex]y = 3x -10[/tex]
Step-by-step explanation:
The function seems to increase at a constant rate of 3 units. This means that the equation that satisfies these points could be that of a straight line.
We use the first two points to find the slope of the line.
(0, -10)
(1, -7)
(2, -4)
The equation of a line is:
[tex]y = mx + b[/tex]
Where m is the slope of the line and b is the cutoff point with the y axis.
To find the slope of a line we use the following equation:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{-7 - (- 10)}{1-0}[/tex]
[tex]m = 3[/tex]
So:
[tex]y = 3x + b[/tex]
The cut point (b) is found by replacing in the previous equation, any of the three points provided and clearing b.
[tex]-7 = 3(1) + b[/tex]
[tex]b = -10[/tex]
Now we can write the equation of the line sought.
[tex]y = 3x -10[/tex]
You can verify that the three points provided belong to this equation.
Answer:
[tex]y=3x-10\\[/tex]
Step-by-step explanation:
An equation that satisfies all the values of a and b as listed is equation of line that passes through points A (0,-10), B (1,-7) and C (2,-4).
To understand this, first of all find points on a graph and connect the points. The result is a straight line passing through A, B and C.
The equation of straight line is given by:
[tex]y= mx +b\\[/tex]
where m is slope of line and b is the y-intercept.
The slope of a line is given as :
[tex]m= dy / dx\\[/tex] where dy is change in y and dx is change in x.
To find slope consider any two points from line. Let us consider A and C for this example. A(0,-10) is starting point of line and C (2,-4) is ending point of line ( we can also consider C as start point. It simply depends on choice).
Therefore, m= -4 -(-10) / 2-0 = -4+10/2= 6/2=3
Slope m= 3
On substituting value of m into equation.
[tex]y= 3x +b\\[/tex]
To find b, take any point A, B or C and simply put the value of y and x into the equation. We do this as A , B and C are simply solutions of the equation and thus can be used.
Taking C and substituting values:
-4= 3*2 + b
b=-10
The resultant equation is as follows:
[tex]y= 3x -10\\[/tex]
