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?

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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

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

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.

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