Question

FIND THE equation of the linear function represented by the table below in slope intercept form

Answer 1

y= -2x - 1

Step-by-step explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

Substitute these points into this formula to find the slope of this linear function.

Simplify and solve for the slope m.

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

Substitute m = -2 and the point (1, -3) into this equation.

Simplify this equation and put it into slope-intercept form: .

The equation of the linear function represented by the table is y = -2x - 1.

Answer 2

y= -2x - 1

Explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

• 
  `\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Substitute these points into this formula to find the slope of this linear function.

• 
  `\displaystyle m= (-5-(-3))/(2-1)`

Simplify and solve for the slope m.

• 
  `\displaystyle m=(-2)/(1) =-2`

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

• 
  `y-y_1=m(x-x_1)`

Substitute m = -2 and the point (1, -3) into this equation.

• 
  `y-(-3)=-2(x-1)`

Simplify this equation and put it into slope-intercept form:
`y=mx+b`.

• 
  `y+3=-2x+2`
• 
  `y=-2x-1`

The equation of the linear function represented by the table is y = -2x - 1.