Find the Line Equation Through Points (5,-11) and (1,9)

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:04 We'll use the formula to find the slope using 2 points

00:10 In each point, the left number represents X-axis and the right Y

00:18 We'll substitute the points according to the given data and find the slope

00:29 This is the line's slope

00:35 Now we'll use the line equation

00:40 We'll substitute the point according to the given data

00:44 We'll substitute the slope and solve to find the intersection point (B)

01:00 We'll isolate the intersection point (B)

01:04 This is the intersection point with the Y-axis

01:11 Now we'll substitute the intersection point and slope in the line equation

01:29 We'll arrange the equation

01:33 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will follow these steps:

Step 1: Calculate the slope of the line passing through the points $(5, -11)$ and $(1, 9)$ .
Step 2: Use the calculated slope and one of the points to determine the equation of the line in point-slope form.
Step 3: Convert the equation to standard form and verify with choices.

Step 1: Calculate the Slope
The slope $m$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - (-11)}{1 - 5} = \frac{9 + 11}{1 - 5} = \frac{20}{-4} = -5$

Step 2: Use Point-Slope Form
We choose point $(1, 9)$ to use in the point-slope formula:

$y - y_1 = m(x - x_1)$
$y - 9 = -5(x - 1)$

Step 3: Simplify to Standard Form
Expand and rearrange the equation:

$y - 9 = -5x + 5$

Bring all terms to one side:

$y + 5x = 14$

The linear equation in standard form is $y + 5x = 14$ , which matches choice 4.