Question

Write the equation parallel to y=5x+1 that passes through (-1,-16).

Answer 1

Answer:

$y = 5x -11$

Explanation:

Given

$y = 5x + 1$ -- equation

$(x,y) = (-1,-16)$

Required

Determine the equation parallel to the given equation and passes through the given point

An equation has a general form:

$y = mx + b$

Where:

$m = slope$

First, we need the slope of the required equation

Since the required equation is parallel to $y = 5x + 1$, then they have the same slope

So, the slope m of the required equation is:

$m = 5$

Next, we determine the equation using:

$y - y_1 = m(x - x_1)$

Where

$m = 5$

$(x,y) = (-1,-16)$

So, we have:

$y - (-16) = 5(x - (-1))$

$y +16 = 5(x +1)$

Open bracket:

$y +16 = 5x +5$

Collect Like Terms

$y = 5x +5 - 16$

$y = 5x -11$