Find the Parallel Line Equation Through Point (-3, -4)

Q: How do I know if two lines are parallel just by looking at their equations?

Lines are parallel if they have identical slopes but different y-intercepts. For example, y = 2x + 3 and y = 2x - 7 are parallel because both have slope 2.

Q: What's the difference between parallel and perpendicular lines?

Parallel lines have the same slope and never intersect. Perpendicular lines have slopes that are negative reciprocals (like 2 and -1/2) and intersect at 90°.

Q: What if the given line isn't in slope-intercept form?

First convert it to y = mx + b form to identify the slope. Then use that same slope with your given point to find the parallel line equation.

Q: How can I double-check my final answer?

Verify that: 1) Your line has the same slope as the given line, and 2) The given point satisfies your equation when substituted in.

Parallel Lines with Point-Slope Formula

Given the line parallel to the line $y=2x-5$

and passes through the point $(-3,-4)$ .

Which of the algebraic representations is the corresponding one for the given line?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's find how to write this function using algebra.

00:15 The line's slope is 2. Remember that.

00:20 Parallel lines always have the same slope.

00:32 Now, we'll use the line equation.

00:35 First, plug in the point from the data.

00:44 Then, use the line's slope you have.

00:51 Keep solving to find where it intersects.

00:57 Focus on isolating the intersection point, called B.

01:04 This is where it crosses the Y-axis.

01:08 Finally, use the intersection point and slope in your equation.

01:24 Great job! You've solved the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the line parallel to the line $y=2x-5$

and passes through the point $(-3,-4)$ .

Which of the algebraic representations is the corresponding one for the given line?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the given line's slope. The given line is $y = 2x - 5$ , which has a slope of $2$ .
Step 2: Since the line we want is parallel, it will have the same slope, $m = 2$ .
Step 3: Use the point-slope formula, $y - y_1 = m(x - x_1)$ . Given point is $(-3, -4)$ .
Step 4: Substitute $m = 2$ , $x_1 = -3$ , and $y_1 = -4$ into the point-slope formula:
$y - (-4) = 2(x - (-3))$
Step 5: Simplify the equation:
$y + 4 = 2(x + 3)$
Step 6: Distribute the $2$ :
$y + 4 = 2x + 6$
Step 7: Solve for $y$ :
$y = 2x + 6 - 4$
Step 8: Simplify further:
$y = 2x + 2$

The corresponding equation of the line parallel to $y = 2x - 5$ and passing through $(-3, -4)$ is $y = 2x + 2$ . When compared to the choices given, the correct choice is:

$y=2x+2$

Final Answer

$y=2x+2$

Key Points to Remember

Essential concepts to master this topic

Parallel Rule: Parallel lines always have identical slopes
Technique: Use point-slope form $y - y_1 = m(x - x_1)$ with given point
Check: Substitute (-3, -4) into y = 2x + 2: -4 = 2(-3) + 2 = -4 ✓

Common Mistakes

Avoid these frequent errors

Using the negative reciprocal slope instead of the same slope
Don't use -1/2 as the slope when finding parallel lines = perpendicular line instead! Negative reciprocal slopes create perpendicular lines, not parallel ones. Always use the exact same slope for parallel lines.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

How do I know if two lines are parallel just by looking at their equations?

Lines are parallel if they have identical slopes but different y-intercepts. For example, y = 2x + 3 and y = 2x - 7 are parallel because both have slope 2.

What's the difference between parallel and perpendicular lines?

Parallel lines have the same slope and never intersect. Perpendicular lines have slopes that are negative reciprocals (like 2 and -1/2) and intersect at 90°.

Do I always need to use point-slope form?

Not always! You can also substitute the point directly into y = mx + b to find b. Both methods work, but point-slope form is often clearer for beginners.

What if the given line isn't in slope-intercept form?

First convert it to y = mx + b form to identify the slope. Then use that same slope with your given point to find the parallel line equation.

How can I double-check my final answer?

Verify that: 1) Your line has the same slope as the given line, and 2) The given point satisfies your equation when substituted in.

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