Question

Find the equation of the linear function represented by the table below in slope-

Answer 1

Answer:

y=5x-4

Step-by-step explanation:

1. Find the slope. Use two ordered pairs from the table and plug them into the slope formula.

Let's use the pairs (1, 1) and (2,6).

Remember, the slope formula is y2-y1/x2-x1.

Let 6 be y2, 1 be y1, 2 be x2 and 1 be x1.

6-1/2-1

This becomes 5/1, or simply 5.

2. Use one of the ordered pairs and the slope to put the equation in point-slope form.

Point-slope form is: y-y1=m(x-x1), with m being the slope, y1 being the y-value in one of the points and x1 being the corresponding x-value.

Let's use the ordered pair (1,1) for this. But, if you used (2,6) you would still get the same answer.

y-1=5(x-1)

3. Finally, convert point-slope to slope-intercept form.

Slope-intercept form is written as y=mx+b with mx being slope and b being the y-intercept.

To convert the point-slope form of the equation to y=mx+b, distribute (or multiply) to x - 1. Then, add 1 to both sides.

Distribute:

y-1=5x-5 (5 times x is 5x and 5 times -1 is -5)

Add 1 to both sides:

y=5x-4