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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).

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

Given the following points:

  • Points on the x-axis = (2, -7)
  • Points on the y-axis = (10, -10)
  • [tex]y = kx + b[/tex]   .....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.

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the points into the formula, we have;

[tex]Slope. \;m = \frac{-10 - 10}{-7 - 2}\\\\Slope. \;m = \frac{-20}{-9}\\\\Slope. \;m = \frac{20}{9}[/tex]

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

[tex]y = mx + b[/tex]   ....equation 2

Where:

  • x and y are the points.
  • m is the slope.
  • b is the intercept.

Next, we would determine the intercept of the graph:

[tex]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}[/tex]

The standard form of this equation of line is:

[tex]y = \frac{20}{9}x - \frac{50}{9}[/tex]    .....equation 3.

Comparing eqn 1 and eqn 3, we can deduce:

[tex]k = \frac{20}{9}[/tex]  and [tex]b = \frac{-50}{9}[/tex]

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

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