What is the equation , , in slope-intercept form , , of the line parallel to y

We are tasked with finding the equation of a line that is parallel to $y = \frac{1}{2}x - 1$ and passes through the point $(4, -3)$.

Step 1: Identify the slope

For a line in slope-intercept form $y = mx + b$, $m$ represents the slope. The slope of the given line $y = \frac{1}{2}x - 1$ is:

$m = \frac{1}{2}$

Since parallel lines have the same slope, the slope of the new line will also be $\frac{1}{2}$.

Step 2: Use the point-slope form of the equation

The point-slope form of the equation of a line is:

$y - y_1 = m(x - x_1)$

where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Here, the slope is $\frac{1}{2}$ and the point is $(4, -3)$.

Substitute these values into the point-slope form:

$y - (-3) = \frac{1}{2}(x - 4)$

This simplifies to:

$y + 3 = \frac{1}{2}(x - 4)$

Step 3: Simplify to slope-intercept form

Now, distribute the $\frac{1}{2}$:

$y + 3 = \frac{1}{2}x - 2$

Subtract 3 from both sides to solve for $y$:

$y = \frac{1}{2}x - 2 - 3$

$y = \frac{1}{2}x - 5$

Final Answer:

The equation of the line in slope-intercept form is:

$y = \frac{1}{2}x - 5$

Would you like further clarification or details on any part of this solution?

Here are 5 related questions to further your understanding:

1. How do you find the slope of a line given two points?
2. What is the general form of the equation of a line?
3. How do you convert from point-slope form to slope-intercept form?
4. What is the significance of parallel and perpendicular lines in geometry?
5. How do you find the equation of a line perpendicular to a given line?

Tip: For parallel lines, always remember that the slopes are the same!