Answer: y = -2x + 9
Step-by-step explanation:
To write the equation of the line, we have to take two points to determine the slope, and then use one of the points to write the equation.
Find two points on the graph
Look at the graph and locate two easy points on the line:
Let (1, 7) be (x₂, y₂)
& (4, 1) be (x₁, y₁)
Determine the slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (7 - 1) ÷ (1 - 4)
= 6 ÷ (-3)
∴ the slope = - 2
Write an equation for the line
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 7 = - 2 (x - 1)
⇒ y = -2x + 2 + 7
∴ an equation for the line is y = -2x + 9
Testing the answer
- If we look at the graph, we realize that the y-intercept would be at (0, 9) as the equation predicts.
- The Desmos graph attached below looks identical to the graph of the equation in the question
