48.5k views
1 vote
A line goes through the points (9,8) and (-3,4).

What is the slope of the line? Show your work
Write the equation of the line in point-slope form. Show your work
Write the equation of the line in slope-intercept form. Show your work.

1 Answer

5 votes

Answer:


\textsf{Slope}: \quad (1)/(3)


\textsf{Point-slope form}: \quad y-8=(1)/(3)(x-9)


\textsf{Slope-intercept form}: \quad y=(1)/(3)x+5

Explanation:


\boxed{\begin{minipage}{4 cm}\underline{Slope formula}\\\\slope ($m$) $=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}

Define the given points:

  • (x₁, y₁) = (9, 8)
  • (x₂, y₂) = (-3, 4)

Substitute the defined points into the slope formula:


\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(4-8)/(-3-9)=(-4)/(-12)=(1)/(3)


\boxed{\begin{minipage}{4.6 cm}\underline{Point-slope formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\end{minipage}}

Substitute point (9, 8) and the found slope into the point-slope formula:


\implies y-8=(1)/(3)(x-9)


\boxed{\begin{minipage}{3.8 cm}\underline{Slope-intercept formula}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\end{minipage}}

To write the equation of the line in slope-intercept form, rearrange the point-slope formula:


\implies y-8=(1)/(3)(x-9)


\implies y-8=(1)/(3)x-3


\implies y-8+8=(1)/(3)x-3+8


\implies y=(1)/(3)x+5

User IAdapter
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories