Find the Equation of a Line Passing Through (3,7) with a Slope of 2y

Q: What does the slope '2y' actually mean in this problem?

The notation '2y' in this context is misleading - it simply means the slope is 2. Don't let the 'y' confuse you! The slope is just the number that tells you how steep the line is.

Q: Why do we use point-slope form instead of slope-intercept form?

Point-slope form is perfect when you know a point and the slope! It's easier than trying to find the y-intercept first. You can always convert to slope-intercept form afterward.

Q: How do I remember the point-slope formula?

Think: 'y minus the y-coordinate equals slope times x minus the x-coordinate'. The formula $ y - y_1 = m(x - x_1) $ literally describes the relationship!

Q: What if I get confused about which number goes where?

Always write down what you know first: Point: $ (3, 7) $ so $ x_1 = 3, y_1 = 7 $Slope: $ m = 2 $Then carefully substitute each value into its proper place.

Q: How can I check if my final answer is correct?

Substitute the given point into your equation! If $ y = 2x + 1 $ is correct, then when $ x = 3 $, we should get $ y = 7 $: $ 7 = 2(3) + 1 = 7 $ ✓

Point-Slope Form with Given Coordinates

A straight line with a slope of 2y passes through the point $(3,7)$ .

Which equation corresponds to the line?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation of the function

00:03 We'll use the straight line equation

00:08 We'll substitute the point according to the given data

00:14 We'll substitute the slope of the line according to the given data

00:20 We'll continue solving to find the intersection point

00:28 We'll isolate intersection point B

00:35 This is the intersection point with the Y-axis

00:39 Now we'll substitute the intersection point and slope in the line equation

00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A straight line with a slope of 2y passes through the point $(3,7)$ .

Which equation corresponds to the line?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Write the equation using point-slope form
Step 2: Substitute the given point and slope into the equation
Step 3: Simplify to find the slope-intercept form of the line equation

Now, let's work through each step:

Step 1: Use the point-slope form of a line equation, given by $y - y_1 = m(x - x_1)$ , where $(x_1, y_1)$ is a point on the line.

Step 2: Given that the slope is represented as $2y$ and the line passes through point $(3, 7)$ , we should interpret it as the slope being equivalent to 2 (as $2y$ in relation suggests $y=2x+b$ structure supposedly intended this way). This gives us a slope $m = 2$ .

Using point $(3, 7)$ , we substitute into the formula:

$y - 7 = 2(x - 3)$

Step 3: Simplify the equation:

$y - 7 = 2x - 6$

$y = 2x - 6 + 7$

$y = 2x + 1$

Therefore, the equation of the line is $y = 2x + 1$ .

Final Answer

$y=2x+1$

Key Points to Remember

Essential concepts to master this topic

Point-Slope Formula: Use $y - y_1 = m(x - x_1)$ with given point
Substitute Values: Replace $(x_1, y_1) = (3, 7)$ and $m = 2$ into formula
Verify Answer: Check that $y = 2x + 1$ gives $7 = 2(3) + 1 = 7$ ✓

Common Mistakes

Avoid these frequent errors

Misinterpreting the slope notation
Don't assume '2y' means the slope involves y = confusing notation! This leads to overcomplicated equations with y on both sides. Always interpret slope as a single number - here the slope is simply 2.

Practice Quiz

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Which statement best describes the graph below?

FAQ

Everything you need to know about this question

What does the slope '2y' actually mean in this problem?

The notation '2y' in this context is misleading - it simply means the slope is 2. Don't let the 'y' confuse you! The slope is just the number that tells you how steep the line is.

Why do we use point-slope form instead of slope-intercept form?

Point-slope form is perfect when you know a point and the slope! It's easier than trying to find the y-intercept first. You can always convert to slope-intercept form afterward.

How do I remember the point-slope formula?

Think: 'y minus the y-coordinate equals slope times x minus the x-coordinate'. The formula $y - y_1 = m(x - x_1)$ literally describes the relationship!

What if I get confused about which number goes where?

Always write down what you know first:

Point: $(3, 7)$ so $x_1 = 3, y_1 = 7$
Slope: $m = 2$

Then carefully substitute each value into its proper place.

How can I check if my final answer is correct?

Substitute the given point into your equation! If $y = 2x + 1$ is correct, then when $x = 3$ , we should get $y = 7$ : $7 = 2(3) + 1 = 7$ ✓

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