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!