Question

What is the equation of this line?

Answer 1

y = 1/2 x -3

Explanation:

the slope is 1/2 (up 1, right 2).

the line crosses the y-axis at (0,-3).

Answer 2

`\textsf{A)} \quad y=(1)/(2)x-3`

Explanation:

`\boxed{\begin{minipage}{8cm}\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 two points on the line:

• Let (x₁, y₁) = (0, -3)
• Let (x₂, y₂) = (2, -2)

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

`\implies \textsf{slope}\:(m)=(-2-(-3))/(2-0)=(-2+3)/(2)=(1)/(2)`

From inspection of the given graph, the line crosses the y-axis at (0, -3). Therefore:

• 
  `\textsf{Slope}=(1)/(2)`

• 
  `\textsf{$y$-intercept}=-3`

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

Substitute the found slope and y-intercept into the formula to create an equation of the line:

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