Answer: y = ³/₄ x - 12
Step-by-step explanation:
Find the slope of the parallel line
When two lines are parallel, they have the same slope.
⇒ if the slope of the given line = ³/₄
then the slope of the parallel line (m) = ³/₄
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line: (12, -3).
⇒ y - (-3) = ³/₄ (x - 12)
y + 3 = ³/₄ (x - 12)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 3 = ³/₄ (x - 12)
y = ³/₄ x - 12
∴ the equation of the line that is parallel to y=3/4x−1 and passes through the point (12, -3) is y = ³/₄ x - 12
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
