Question

A liner function of x is graphed on a coordinate grid. the points 6,34 and 18,26 lie on the graph of the function what are the rate of change of the function and the value of the function the x=24
please show or explain the work so l can understand

Answer 1

Answer:

Rate of change: m = -2/3

Value of the function at x = 24: y = 22

Step-by-step explanation:

You can write linear functions in slope-intercept form: y = mx + b

"x" and "y" are points on the line

"m" is the slope, how steep the line is, also known as rate of change

"b" is the y-intercept, when the graph hits the y-axis

Find the rate of change of the function by finding the slope between the two given points.

The formula for slope: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Label point 1 and point 2. Label each coordinate; remembered ordered pairs are (x, y).

Point 1      (6, 34)         x₁= 6   y₁ = 34

Point 2     (18, 26)        x₂ = 18   y₂ = 26

Substitute the points into your equation using the bolded information.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{26-34}{18-6}$       Subtract

$=\frac{-8}{12}$             Reduce the fraction. Top and bottom divide by 4

$=\frac{-2}3}$              Slope of the line, "m"

Substitute the slope and any point you want into slope-intercept form. I choose point (6, 34). x = 6    y = 34   m = -2/3

y = mx + b

34 = (-2/3)(6) + b                      Multiply to simplify

34 = (-12/3) + b

Start isolating "b"

34 + 12/3 = (-12/3) + 12/3 + b              Add 12/3 on both sides

34 + 12/3 = b

Add fractions by combining the whole number into the numerator. Multiply the whole number by the denominator and add to the numerator.

b = (34*3 + 12) / 3              Solve numerator

b = 114/3                      Value of "b"

Substitute the values "m" and "b" into slope-intercept form.

y = -2/3 x + 114/3                  Equation of the line

To find the x = 24, take the equation of the line and substitute "x" for 24. Then solve for "y".

y = -2/3 x + 114/3                       Equation of the line

y = (-2/3)(24) + 114/3

y = (-2*24)/3  + 114/3                     Multiply into the numerator

y = (-48)/3 + 114/3                       Combine under the same denominator

y = (-48 + 114) / 3                      Add

y = 66/3                        Divide

y = 22                      Value of function

Therefore the rate of change, or slope "m", is -2/3. When "x" is 24, the value of the entire function is 22.