Identify the Line Equation with Slope 9y Passing Through (-5, -8)

Q: Why do we use point-slope form instead of slope-intercept form directly?

When you have a point and slope, point-slope form $ y - y_1 = m(x - x_1) $ is the most direct method. You can convert to slope-intercept form $ y = mx + b $ afterward if needed.

Q: How do I handle the double negatives in the substitution?

Remember: subtracting a negative is adding a positive. So $ y - (-8) = y + 8 $ and $ x - (-5) = x + 5 $. Take your time with the signs!

Q: What if I get a different form than the answer choices?

That's okay! You might need to expand and simplify your equation. For example, $ y + 8 = 9(x + 5) $ becomes $ y = 9x + 37 $ after distributing and isolating y.

Q: How can I check if my final equation is correct?

Substitute the given point into your final equation. For $ y = 9x + 37 $, plug in $ (-5, -8) $: Does $ -8 = 9(-5) + 37 $? Yes, $ -8 = -45 + 37 = -8 $ ✓

Q: Can I start with slope-intercept form if I know the slope?

You could try $ y = 9x + b $ and solve for b using the point, but point-slope form is usually faster and less error-prone when you have a specific point.

Point-Slope Form with Given Coordinates

A straight line with the slope 9 passes through the point $(-5,-8)$ .

Which of the following equations corresponds to the line?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation of the function

00:03 We'll use the straight line equation

00:09 We'll substitute the point according to the given data

00:15 We'll substitute the slope according to the given data

00:19 We'll continue solving to find the intersection point

00:30 We'll isolate intersection point B

00:36 This is the intersection point with the Y-axis

00:41 Now we'll substitute the intersection point and slope in the line equation

00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A straight line with the slope 9 passes through the point $(-5,-8)$ .

Which of the following equations corresponds to the line?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the point-slope formula
Step 3: Convert to slope-intercept form and verify against the given choices

Now, let's work through each step:
Step 1: The problem states the line passes through point $(-5, -8)$ and has a slope of $9$ .
Step 2: Using the point-slope form equation, $y-y_1 = m(x-x_1)$ , plug in $(x_1, y_1) = (-5, -8)$ and $m = 9$ . So the equation becomes:

y - (-8) = 9(x - (-5))

Which simplifies to:

y + 8 = 9(x + 5)

Simplifying further gives:

y + 8 = 9x + 45

Then, bring the $8$ to the right side to solve for $y$ in terms of $x$ :

y = 9x + 45 - 8

y = 9x + 37

Therefore, the equation of the line in slope-intercept form is $y = 9x + 37$ , which corresponds to choice $1$ .

Therefore, the solution to the problem is $y = 9x + 37$ .

Final Answer

$y=9x+37$

Key Points to Remember

Essential concepts to master this topic

Formula: Use point-slope form $y - y_1 = m(x - x_1)$ with given values
Technique: Substitute $(-5, -8)$ and $m = 9$ to get $y + 8 = 9(x + 5)$
Check: Verify final answer by plugging point back: $-8 = 9(-5) + 37 = -8$ ✓

Common Mistakes

Avoid these frequent errors

Sign errors when substituting negative coordinates
Don't write $y - (-8) = 9(x - (-5))$ as $y - 8 = 9(x - 5)$ = wrong signs! Negative minus negative becomes positive: $y - (-8) = y + 8$ . Always be extra careful with double negatives when substituting coordinates.

Practice Quiz

Test your knowledge with interactive questions

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

FAQ

Everything you need to know about this question

Why do we use point-slope form instead of slope-intercept form directly?

When you have a point and slope, point-slope form $y - y_1 = m(x - x_1)$ is the most direct method. You can convert to slope-intercept form $y = mx + b$ afterward if needed.

How do I handle the double negatives in the substitution?

Remember: subtracting a negative is adding a positive. So $y - (-8) = y + 8$ and $x - (-5) = x + 5$ . Take your time with the signs!

What if I get a different form than the answer choices?

That's okay! You might need to expand and simplify your equation. For example, $y + 8 = 9(x + 5)$ becomes $y = 9x + 37$ after distributing and isolating y.

How can I check if my final equation is correct?

Substitute the given point into your final equation. For $y = 9x + 37$ , plug in $(-5, -8)$ : Does $-8 = 9(-5) + 37$ ? Yes, $-8 = -45 + 37 = -8$ ✓

Can I start with slope-intercept form if I know the slope?

You could try $y = 9x + b$ and solve for b using the point, but point-slope form is usually faster and less error-prone when you have a specific point.

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