Find the Line Equation: Parallel to 5y-5x=15 Through Point (-5,12)

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:03 Isolate Y

00:16 This is the equation of the parallel function

00:20 This is the slope of the parallel function

00:23 Parallel functions have equal slopes

00:28 Let's use the line equation

00:31 Substitute the point according to the given data

00:36 Substitute the slope and solve to find the intersection point (B)

00:55 Isolate the intersection point (B)

01:01 This is the intersection point with the Y-axis

01:14 Now substitute the intersection point and slope in the line equation

01:26 Arrange the equation

01:30 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Let's work through each step:

Step 1: Determine the slope of the given line.
First, convert the equation $5y - 5x = 15$ to slope-intercept form ( $y = mx + b$ ):

Divide every term by 5 to simplify:
$5y = 5x + 15$
$y = x + 3$

The slope ( $m$ ) of this line is $1$ .

Step 2: Use the point-slope form with the given point and slope.
We have a point $(-5, 12)$ and a slope $m = 1$ . The point-slope form is:

$y - y_1 = m(x - x_1)$
Substitute $y_1 = 12$ , $x_1 = -5$ , and $m = 1$ :
$y - 12 = 1(x + 5)$

Simplify the equation:
$y - 12 = x + 5$

Step 3: Rearrange to get the solution.
Rearrange the equation:
$y = x + 5 + 12$
$y = x + 17$

We want to express this in the form of one of the given choices:
$y - x = 17$ .

Therefore, the solution to the problem is $y - x = 17$ .

This matches the final answer choice given in the problem, confirming our solution is correct.