Find the Line Equation: Parallel to 2(y+1)=16x Through Point (0,1)

Q: Why do parallel lines have the same slope?

Parallel lines never intersect, which means they rise and fall at exactly the same rate. The slope measures this rate of change, so parallel lines must have identical slopes.

Q: How do I convert 2(y+1)=16x to slope-intercept form?

First distribute: $ 2y + 2 = 16x $. Then isolate y: $ 2y = 16x - 2 $. Finally divide by 2: $ y = 8x - 1 $.

Q: What if I used point-slope form instead?

Point-slope form works great! Using $ y - 1 = 8(x - 0) $ gives you $ y - 1 = 8x $, which rearranges to $ y - 8x = 1 $.

Q: How can I check if my line is really parallel?

Compare the slopes only. If both lines have slope = 8, they're parallel. The y-intercepts should be different - if they're the same, the lines are identical!

Parallel Lines with Point-Slope Form

Straight line passes through the point $(0,1)$ and parallel to the line $2(y+1)=16x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the algebraic representation of the function.

00:14 First, open the parentheses properly and multiply each factor. Take your time with this step.

00:24 Next, let's isolate Y. Focus on getting Y by itself on one side of the equation.

00:31 You've got it! This is the equation of the parallel function.

00:35 Remember, this is the slope of the parallel function.

00:39 Parallel functions have equal slopes, keep that in mind.

00:44 Let's use the line equation, which is a handy tool here.

00:48 Substitute the point according to the given data. You're doing great!

00:53 Now, substitute the slope and solve to find the intersection point, the point B.

01:02 This is the intersection point with the Y-axis.

01:10 Now, substitute this intersection point and the slope in the line equation.

01:23 Finally, arrange the equation nicely.

01:31 And there you have it, the solution to the question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Straight line passes through the point $(0,1)$ and parallel to the line $2(y+1)=16x$

Step-by-step solution

To solve for the equation of the line parallel to $2(y+1)=16x$ that passes through the point $(0,1)$ , follow these steps:

Step 1: Convert the given line's equation to slope-intercept form. Start with $2(y+1) = 16x$ .
Step 2: Distribute and simplify to get $2y + 2 = 16x$ , which rearranges to $2y = 16x - 2$ .
Step 3: Solve for $y$ by dividing everything by 2: $y = 8x - 1$ . Hence, the slope $m$ is 8.
Step 4: Use the slope of 8 and the point $(0,1)$ in the point-slope form of a line equation:
$\quad y - y_1 = m(x - x_1)$
Step 5: Substitute the point $(0,1)$ and the slope $8$ :
$\quad y - 1 = 8(x - 0)$
Step 6: Simplify the expression
$\quad y - 1 = 8x$
Step 7: Rewrite the equation to achieve the desired form by moving 1 to the other side:
$\quad y = 8x + 1$
Step 8: To match the expected form, rewrite
$y - 8x = 1$

Therefore, the equation of the line that meets the criteria is given by $y - 8x = 1$ , corresponding to choice 3.

Final Answer

$y-8x=1$

Key Points to Remember

Essential concepts to master this topic

Rule: Parallel lines have identical slopes but different y-intercepts
Technique: Convert $2(y+1)=16x$ to slope-intercept form to find slope = 8
Check: Substitute (0,1): 1 - 8(0) = 1 gives 1 = 1 ✓

Common Mistakes

Avoid these frequent errors

Using the original equation's y-intercept
Don't use the y-intercept from $y = 8x - 1$ for the new line = wrong equation! The original line passes through (0,-1), not (0,1). Always find the new y-intercept using the given point.

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, which means they rise and fall at exactly the same rate. The slope measures this rate of change, so parallel lines must have identical slopes.

How do I convert 2(y+1)=16x to slope-intercept form?

First distribute: $2y + 2 = 16x$ . Then isolate y: $2y = 16x - 2$ . Finally divide by 2: $y = 8x - 1$ .

Why is the answer y - 8x = 1 and not y = 8x + 1?

Both forms are mathematically correct! The question asks for the specific form that matches the given choices. $y - 8x = 1$ is just rearranged from $y = 8x + 1$ .

What if I used point-slope form instead?

Point-slope form works great! Using $y - 1 = 8(x - 0)$ gives you $y - 1 = 8x$ , which rearranges to $y - 8x = 1$ .

How can I check if my line is really parallel?

Compare the slopes only. If both lines have slope = 8, they're parallel. The y-intercepts should be different - if they're the same, the lines are identical!

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