Answer: y - 3 = ²/₃ (x - 6) OR y = ²/₃ x - 1
Step-by-step explanation:
For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:
The question gives a graph with two highlighted points that we can use to find the slope and later the equation of the line: (6, 3) and (0, -1).
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (3 - (-1)) ÷ (6 - 0)
= ²/₃
Finding the Equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line; where (x₁ , y₁) = (6, 3):
⇒ y - 3 = ²/₃ (x - 6)
we could also transform this into the slope-intercept form ( y = mx + c)
since y - 3 = ²/₃ (x - 6)
y - 3 = ²/₃ x - ²/₃ (6)
y = ²/₃ x - 4 + 3
⇒ y = ²/₃ x - 1
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
