Answer: y - 12 = 5 (x - 4) OR y = 5x - 8
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 us two points, (4,12) and (−1,−13), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (12 - (- 13)) ÷ (4 - (- 1))
= 25 ÷ 5
= 5
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) = (4, 12):
⇒ y - 12 = 5 (x - 4)
we could also transform this into the slope-intercept form ( y = mx + c)
since y - 12 = 5 (x - 4)
y - 12 = 5x + 5 (-4)
y = 5x - 20 + 12
⇒ y = 5x - 8
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
