Find the Linear Equation Through Points (9,10) and (99,100): Step-by-Step

Video Solution

Solution Steps

00:00 Find the algebraic representation for function

00:04 Use formula to find slope using 2 points

00:12 In each point, left number represents X-axis and right Y

00:17 Plot points according to data and find slope

00:31 This is the line's slope

00:34 Now use the line equation

00:38 Plot point according to data

00:43 Plot slope and solve to find intersection point (B)

00:55 Isolate intersection point (B)

01:02 This is the intersection point with Y-axis

01:08 Now plot intersection point and slope in line equation

01:24 This is the solution to the question

Step-by-Step Solution

To find the equation of the line passing through the points $(9, 10)$ and $(99, 100)$ , follow these steps:

Step 1: Determine the slope, $m$ , of the line.
Step 2: Use one point and the calculated slope to find the equation of the line.
Step 3: Simplify to find the line's equation in slope-intercept form.

Step 1: Calculate the slope $m$ using the formula:
$m = \frac{100 - 10}{99 - 9} = \frac{90}{90} = 1$ .

Step 2: Now, use the point $(9, 10)$ and the point-slope form:
$y - 10 = 1 \cdot (x - 9)$ .

Step 3: Simplify this equation:
$y - 10 = x - 9$
$y = x + 1$ .

Thus, the equation of the line is $y = x + 1$ , matching answer choice (2).