Question

What is the equation of this line?

Answer 1

Answer:

y = 1/2 x -3

Step-by-step explanation:

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

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

Answer 2

Answer:

$\textsf{A)} \quad y=\dfrac{1}{2}x-3$

Step-by-step explanation:

$\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope (m)=\dfrac{y_2-y_1}{x_2-x_1} \\\\where (x_1,y_1) and (x_2,y_2) are two points on the line.\\\end{minipage}}$

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:

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

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

• $\textsf{Slope}=\dfrac{1}{2}$

• $\textsf{ y -intercept}=-3$

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

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

$\implies y=\dfrac{1}{2}x-3$