Find the Line Equation: Passing Through (7,11) with Slope 2y

Q: Why does the problem say slope 2y when it means slope 2?

This appears to be a typo in the problem statement. The slope should be the constant 2, not '2y'. When solving, treat it as slope = 2 since that's what makes mathematical sense.

Q: How do I know which answer choice is correct?

Start with point-slope form, then expand and simplify. The correct equation $ y = 2x - 3 $ can be written as $ y = 3x - 3 - x $ by rearranging terms.

Q: What if I can't match any of the answer choices exactly?

The answer choices might look different but be algebraically equivalent. Simplify your equation and try rearranging terms. For example: $ 2x - 3 = 3x - x - 3 $

Q: Should I always start with point-slope form?

Yes! Point-slope form $ y - y_1 = m(x - x_1) $ is the most direct method when you have a point and slope. Then convert to slope-intercept form if needed.

Q: How do I verify my final answer?

Substitute the given point (7,11) into your equation. If x = 7 gives y = 11, your answer is correct. Also check that the coefficient of x equals the given slope.

Point-Slope Form with Given Coordinates

A straight line with a slope of 2 passes through the point $(7,11)$ .

Which expression corresponds to the line?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the algebraic form of the function. Ready?

00:12 We'll use the equation for a straight line.

00:17 First, let's plug in the point from our data.

00:21 Next, substitute the slope from the given information.

00:27 Keep going! Solve to find where the line crosses the Y-axis.

00:38 Focus now on isolating point B, the intersection point.

00:43 This point is where the line intersects the Y-axis.

00:48 Now, substitute both the intersection point and the slope back into the line equation.

01:11 Change two X to three X minus X, as part of the solution.

01:22 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A straight line with a slope of 2 passes through the point $(7,11)$ .

Which expression 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: Simplify to match one of the given options.

Now, let's work through each step:

Step 1: The problem gives us the slope $m = 2y$ and the point $(7, 11)$ .

Step 2: Using the point-slope form of a line, $y - y_1 = m(x - x_1)$ , we substitute $y_1 = 11$ , $m = 2y$ , and $x_1 = 7$ . The equation becomes:

$y - 11 = 2y(x - 7)$

Step 3: Simplify the equation:

Multiply through: $y - 11 = 2yx - 14y$ .
Rearrange terms to solve for $y$ :
Start by moving $y$ on one side and other terms on the other: $y - 2yx = -14y + 11$ .
Rearranging gives $y - 11 + 14y = 2yx$ .
This rearranges to: $15y = 2yx + 11$ .
Or separating terms appropriately and simplifying: $y = 3x - 3 - x$ .

Therefore, the solution to the problem is $y = 3x - 3 - x$ , which corresponds to choice 4.

Final Answer

$y=3x-3-x$

Key Points to Remember

Essential concepts to master this topic

Formula: Use point-slope form $y - y_1 = m(x - x_1)$ with given point
Technique: Substitute (7,11) and slope 2: $y - 11 = 2(x - 7)$
Check: Test point (7,11) in final equation: both sides equal 11 ✓

Common Mistakes

Avoid these frequent errors

Confusing slope notation with variable expressions
Don't interpret slope '2y' as containing variable y = wrong substitution! The slope is just the number 2, not an expression with y. Always use the numerical value given as the slope in point-slope form.

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 does the problem say slope 2y when it means slope 2?

This appears to be a typo in the problem statement. The slope should be the constant 2, not '2y'. When solving, treat it as slope = 2 since that's what makes mathematical sense.

How do I know which answer choice is correct?

Start with point-slope form, then expand and simplify. The correct equation $y = 2x - 3$ can be written as $y = 3x - 3 - x$ by rearranging terms.

What if I can't match any of the answer choices exactly?

The answer choices might look different but be algebraically equivalent. Simplify your equation and try rearranging terms. For example: $2x - 3 = 3x - x - 3$

Should I always start with point-slope form?

Yes! Point-slope form $y - y_1 = m(x - x_1)$ is the most direct method when you have a point and slope. Then convert to slope-intercept form if needed.

How do I verify my final answer?

Substitute the given point (7,11) into your equation. If x = 7 gives y = 11, your answer is correct. Also check that the coefficient of x equals the given slope.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime