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

Q: Why does it matter which point I use in point-slope form?

It doesn't matter which point you choose! Whether you use (9,10) or (99,100), you'll get the same final equation. The math works out the same way because both points lie on the same line.

Q: How do I remember the slope formula correctly?

Think "rise over run" - how much the line goes up (or down) divided by how much it goes across. Always keep the same order: if you use the first y-coordinate on top, use the first x-coordinate on bottom.

Q: What if I get a negative slope?

That's perfectly normal! A negative slope just means the line goes downward as you move from left to right. In this problem, we got a positive slope of 1, so our line goes upward.

Q: What does the +1 in y = x + 1 represent?

The +1 is the y-intercept - it's where the line crosses the y-axis. This means when x = 0, y = 1, so the line passes through point (0,1).

Linear Equations with Point-Slope Form

Find the equation of the line passing through the two points $(9,10),(99,100)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the equation of the line passing through the two points $(9,10),(99,100)$

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).

Final Answer

$y=x+1$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ to find the line's steepness
Point-Slope Form: Apply $y - y_1 = m(x - x_1)$ using either given point
Verification: Substitute both original points into final equation to confirm they satisfy it ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinates when calculating slope
Don't randomly subtract coordinates like $\frac{10-100}{99-9}$ = wrong slope! This creates the wrong steepness and completely wrong equation. Always keep coordinates organized: subtract y-values together and x-values together in the same order.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Why does it matter which point I use in point-slope form?

It doesn't matter which point you choose! Whether you use (9,10) or (99,100), you'll get the same final equation. The math works out the same way because both points lie on the same line.

How do I remember the slope formula correctly?

Think "rise over run" - how much the line goes up (or down) divided by how much it goes across. Always keep the same order: if you use the first y-coordinate on top, use the first x-coordinate on bottom.

What if I get a negative slope?

That's perfectly normal! A negative slope just means the line goes downward as you move from left to right. In this problem, we got a positive slope of 1, so our line goes upward.

Can I check my answer without graphing?

Absolutely! Just substitute both original points into your final equation. For $y = x + 1$ : Point (9,10) gives 10 = 9 + 1 ✓ and point (99,100) gives 100 = 99 + 1 ✓

What does the +1 in y = x + 1 represent?

The +1 is the y-intercept - it's where the line crosses the y-axis. This means when x = 0, y = 1, so the line passes through point (0,1).

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