Question

What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?

y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)

Answer 1

`\textsf{B)} \quad y-9=2(x-2)`

Explanation:

`\boxed{\begin{minipage}{9cm}\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}}`

Given points:

• (-3, -1)
• (2, 9)

Substitute the given points into the slope formula to find the slope of the line:

`\implies m=(9-(-1))/(2-(-3))=(10)/(5)=2`

`\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}}`

Substitute the found slope and point (-3, -1) into the point-slope formula:

`\implies y-(-1)=2(x-(-3))`

`\implies y+1=2(x+3)`

Substitute the found slope and point (2, 9) into the point-slope formula:

`\implies y-9=2(x-2)`

Therefore, the correct answer option is:

`\textsf{B)} \quad y-9=2(x-2)`