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Huuuurrry plllzzzzzz. Determine the equation of the line that passes through the given points (2,6) and (4,16)

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theleangreenbean

Linear Equations

Linear equations are typically organized in slope-intercept form:

[tex]y=mx+b[/tex]

  • m is the slope of the line
  • b is the y-intercept (the value of y when the line passes through the y-axis)

To find linear equations in slope-intercept form:

  1. Determine the slope
  2. Plug the slope into the general form
  3. Determine the y-intercept by isolating b
  4. Plug the b back into the equation

Solving the Question

We're given:

  • The line passes through the points (2,6) and (4,16)

First, determine the slope of the line.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line

⇒ Plug in the given points (2,6) and (4,16):

[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]

⇒ Therefore, the slope of the line is 5. Plug this back into the general form:

[tex]y=5x+b[/tex]

Now, determine the y-intercept.

[tex]y=5x+b[/tex]

⇒ Plug in one of the given points:

[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]

⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:

[tex]y=5x-4[/tex]

Answer

[tex]y=5x-4[/tex]

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