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

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).