Find the Line Equation: Parallel to -4+y=5x-6 Through (-2,-13)

Q: Why do parallel lines have the same slope?

Parallel lines never intersect because they rise and fall at exactly the same rate. This rate of change is the slope, so parallel lines must have identical slopes!

Q: How do I find the slope from -4 + y = 5x - 6?

First solve for y: add 4 to both sides to get y = 5x - 6 + 4, which simplifies to $ y = 5x - 2 $. The slope is the coefficient of x, which is 5.

Q: What's the difference between this line and the original?

Both lines have slope = 5, but different y-intercepts. The original line crosses the y-axis at -2, while our new line crosses at -3. Same steepness, different position!

Q: Can I use point-slope form instead?

Absolutely! Using $ y - y_1 = m(x - x_1) $ gives: $ y - (-13) = 5(x - (-2)) $, which simplifies to the same answer: $ y = 5x - 3 $.

Parallel Lines with Point-Slope Form

Choose the function for a straight line that passes through the point $(-2,-13)$ and is parallel to the line $-4+y=5x-6$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's find the algebraic form of the function.

00:14 First, we'll isolate Y. Here's how to do it.

00:24 This is the equation of our parallel function.

00:27 And this represents the slope of that parallel function.

00:31 Remember, parallel functions always have the same slopes.

00:35 Next, we'll use the line equation. Let's get started.

00:39 We'll substitute the given point into the equation based on the data.

00:48 Then, substitute the slope, and solve to find the intersection point, B.

01:01 Let's isolate B, the intersection point, in this step.

01:10 This point is where it intersects the Y-axis.

01:18 Now, plug the intersection point and slope back into the line equation.

01:29 And there you go, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the function for a straight line that passes through the point $(-2,-13)$ and is parallel to the line $-4+y=5x-6$ .

Step-by-step solution

First, write out the line equations:

$-4+y=5x-6$

$y=5x+4-6$

$y=5x-2$

From here we can determine the slope:

$m=5$

We'll use the formula:

$y=mx+b$

We'll use the point $(-2,-13)$ :

$-13=5\times-2+b$

$-13=-10+b$

$-3=b$

Finally, substitute our data back into the formula:

$y=5x+(-3)$

$y=5x-3$

Final Answer

$y=5x-3$

Key Points to Remember

Essential concepts to master this topic

Parallel Lines: Same slope as original line equation
Technique: Use $y = mx + b$ with point (-2, -13)
Check: Substitute point into final equation: -13 = 5(-2) - 3 ✓

Common Mistakes

Avoid these frequent errors

Using wrong slope from given equation
Don't use slope before simplifying -4 + y = 5x - 6 = wrong slope! The equation must be in y = mx + b form first to identify slope correctly. Always rearrange to y = 5x - 2 to see slope is 5.

Practice Quiz

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Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Why do parallel lines have the same slope?

Parallel lines never intersect because they rise and fall at exactly the same rate. This rate of change is the slope, so parallel lines must have identical slopes!

How do I find the slope from -4 + y = 5x - 6?

First solve for y: add 4 to both sides to get y = 5x - 6 + 4, which simplifies to $y = 5x - 2$ . The slope is the coefficient of x, which is 5.

What's the difference between this line and the original?

Both lines have slope = 5, but different y-intercepts. The original line crosses the y-axis at -2, while our new line crosses at -3. Same steepness, different position!

Can I use point-slope form instead?

Absolutely! Using $y - y_1 = m(x - x_1)$ gives: $y - (-13) = 5(x - (-2))$ , which simplifies to the same answer: $y = 5x - 3$ .

How do I check if my answer is correct?

Substitute the given point (-2, -13) into your equation. For $y = 5x - 3$ : -13 = 5(-2) - 3 = -10 - 3 = -13 ✓. Perfect match!

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