write the equation of the line parallel to 2x-y=7 that passes through the point(-3,4)

To find the equation of a line that is parallel to \(2x - y = 7\) and passes through the point \((-3, 4)\), follow these steps:

### Step 1: Find the slope of the given line
The equation \(2x - y = 7\) can be rewritten in slope-intercept form (\(y = mx + b\)) to find the slope. Start by solving for \(y\):

\[
2x - y = 7
\]
\[
-y = -2x + 7
\]
\[
y = 2x - 7
\]

So, the slope of the given line is \(m = 2\).

### Step 2: Use the slope for the new line
Since parallel lines have the same slope, the slope of the new line will also be \(m = 2\).

### Step 3: Apply the point-slope form
The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \(m = 2\) (the slope),
- \((x_1, y_1) = (-3, 4)\) (the given point).

Substitute these values into the point-slope form:

\[
y - 4 = 2(x + 3)
\]

### Step 4: Simplify the equation
Now, simplify the equation to get the slope-intercept form (\(y = mx + b\)):

\[
y - 4 = 2x + 6
\]
\[
y = 2x + 6 + 4
\]
\[
y = 2x + 10
\]

### Final Answer:
The equation of the line parallel to \(2x - y = 7\) and passing through \((-3, 4)\) is:

\[
y = 2x + 10
\]

Would you like a detailed explanation of any step?

### 5 Related Questions:
1. How do you find the equation of a line perpendicular to \(2x - y = 7\)?
2. What is the slope-intercept form of a line?
3. How do you find the distance between a point and a line?
4. How do you convert an equation from point-slope form to slope-intercept form?
5. What is the significance of the slope in parallel lines?

### Tip:
When working with parallel lines, always remember that their slopes are equal!

Learn how to find the equation of a line parallel to 2x - y = 7 that passes through the point (-3, 4). This problem covers key algebraic concepts such as parallel lines and the point-slope form. Suitable for students in Grades 9-10.

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