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

Video Solution

Solution Steps

00:07 Let's begin by finding the algebraic form of the function.

00:12 We'll use a handy formula to find the slope using two points.

00:17 Remember: in each point, the first number is the X-value, and the second is the Y-value.

00:25 Let's substitute the points into the formula to find our slope.

00:36 And here we have the slope of the line.

00:42 Next, we will use the line equation.

00:47 Plug in the given point into the equation.

00:51 Now substitute the slope, and calculate to find the intercept, B.

01:07 Let's isolate the intercept, B.

01:11 Here is the intercept point on the Y-axis.

01:18 Finally, put the intercept and slope back into the line equation.

01:36 Let's tidy up the equation.

01:40 And there you have it! That's 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.