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A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

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Answer :

semsee45

Answer:

[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.

Define the points:

  • (x₁, y₁) = (10, 6)
  • (x₂, y₂) = (2, 7)

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]

Therefore, the slope of the line is -¹/₈.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]

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