Which equation satisfies all three pairs of a and b values listed in the table? a b 0 -10 1 -7 2 -4

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:

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:

So:

The cut point (b) is found by replacing in the previous equation, any of the three points provided and clearing b.

Now we can write the equation of the line sought.

You can verify that the three points provided belong to this equation.

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:

where m is slope of line and b is the y-intercept.

The slope of a line is given as :

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.

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:

b

step-by-step explanation: