Please select the word from the list that best fits the definition ages 85 and older.

Find the values of k and b if it is known that the graph of y=kx b goes through points (2, 10) and (−7, −10).

andreev551 [17]

The values of k and b of this graph that passes through the given points is $k = \frac{20}{9}$ and $b = \frac{-50}{9}$

<u>Given the following points:</u>

Points on the x-axis = (2, -7)

Points on the y-axis = (10, -10)

$y = kx + b$ .....equation 1.

To find the values of k and b since the graph passes through the given points:

First of all, we would determine the slope of the graph passing through the given points.

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points into the formula, we have;

$Slope. \;m = \frac{-10 - 10}{-7 - 2}\\\\Slope. \;m = \frac{-20}{-9}\\\\Slope. \;m = \frac{20}{9}$

The standard form of an equation of line is given by the formula;

$y = mx + b$ ....equation 2

<u>Where:</u>

x and y are the points.

m is the slope.

b is the intercept.

Next, we would determine the intercept of the graph:

$10 = \frac{20}{9}(2) + b\\\\10 = \frac{40}{9} + b\\\\b = \frac{40}{9} - 10\\\\b = \frac{40\; - \;90}{9}\\\\b = \frac{-50}{9}$

The standard form of this equation of line is:

$y = \frac{20}{9}x - \frac{50}{9}$ .....equation 3.

Comparing eqn 1 and eqn 3, we can deduce:

$k = \frac{20}{9}$ and $b = \frac{-50}{9}$

Therefore, the values of k and b of this graph that passes through the given points is $k = \frac{20}{9}$ and $b = \frac{-50}{9}$

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