Determine the Linear Equation: Slope -3 Through Point (-6, -3)

Q: How do I remember the point-slope formula?

Remember: y - y₁ = m(x - x₁). The subscript 1 means "the given point" and m is always the slope. You're finding how far any point (x,y) is from your known point.

Q: What if I get confused with all the negative signs?

Write it step by step! First substitute: y - (-3) = -3(x - (-6)). Then simplify the double negatives: y + 3 = -3(x + 6). Take your time with each sign.

Q: Can I use slope-intercept form directly?

You could use y = mx + b and solve for b, but point-slope form is more direct when you're given a point and slope. It saves steps!

Point-Slope Form with Negative Coordinates

A linear function has a slope of -3 and passes through the point $(-6,-3)$ .

Choose the equation that represents the function.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function equations

00:10 We'll use the line equations

00:16 We'll substitute appropriate values according to the given data and solve for B

00:39 Isolate B

00:49 This is the value of B

00:54 Now we'll substitute and find the line equation

01:06 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 linear function has a slope of -3 and passes through the point $(-6,-3)$ .

Choose the equation that represents the function.

Step-by-step solution

To determine the equation of the given linear function, follow these steps:

Step 1: Identify the key information: the slope $m = -3$ and the point $(-6, -3)$ .
Step 2: Use the point-slope form, $y - y_1 = m(x - x_1)$ .
Step 3: Substitute the values $m = -3$ , $x_1 = -6$ , and $y_1 = -3$ into the formula.
Step 4: Solve for $y$ to convert to slope-intercept form $y = mx + b$ .

Now, let's go through the process:

Use the point-slope form:

$y - (-3) = -3(x - (-6))$

Simplify the equation:

$y + 3 = -3(x + 6)$

Distribute the slope on the right side:

$y + 3 = -3x - 18$

Subtract 3 from both sides to solve for $y$ :

$y = -3x - 18 - 3$

which simplifies to:

$y = -3x - 21$

This equation, $y = -3x - 21$ , matches the first choice in the provided options.

Therefore, the equation that represents the function is $y = -3x - 21$ .

Final Answer

$y=-3x-21$

Key Points to Remember

Essential concepts to master this topic

Point-Slope Formula: Use y - y₁ = m(x - x₁) with given values
Double Negative Rule: x - (-6) becomes x + 6, y - (-3) becomes y + 3
Verification: Substitute (-6, -3) into y = -3x - 21: -3 = -3(-6) - 21 = -3 ✓

Common Mistakes

Avoid these frequent errors

Sign errors when substituting negative coordinates
Don't write y - (-3) = -3(x - (-6)) as y - 3 = -3(x - 6) = wrong signs! Negative minus negative becomes positive. Always use y + 3 = -3(x + 6) when substituting negative coordinates.

Practice Quiz

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For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

Why does x - (-6) become x + 6?

When you subtract a negative number, it becomes addition! Think of it as subtracting negative 6 which equals adding positive 6. So x - (-6) = x + 6.

How do I remember the point-slope formula?

Remember: y - y₁ = m(x - x₁). The subscript 1 means "the given point" and m is always the slope. You're finding how far any point (x,y) is from your known point.

What if I get confused with all the negative signs?

Write it step by step! First substitute: y - (-3) = -3(x - (-6)). Then simplify the double negatives: y + 3 = -3(x + 6). Take your time with each sign.

Can I use slope-intercept form directly?

You could use y = mx + b and solve for b, but point-slope form is more direct when you're given a point and slope. It saves steps!

How do I check if my final equation is correct?

Substitute your given point into the final equation. For (-6, -3): -3 = -3(-6) - 21. If you get -3 = 18 - 21 = -3 ✓, you're right!

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