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

Which statement best describes the graph below?

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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