
What is the equation
,
, in slope-intercept form
,
, of the line parallel to 
y
=
1
2
x
−
1
y= 
2
1
​
 x−1 that passes through the point with coordinates 
(
4
,
−
3
)
?
(4,−3)?  





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!

What is the equation, in slope-intercept form, of the line parallel to y = 1/2x - 1 that passes through the point with coordinates (4, -3)?

Discover how to find the equation of a line parallel to y = 1/2x - 1 that passes through the point (4, -3). This detailed solution covers key algebraic concepts like slope-intercept form and point-slope form, making it suitable for students in Grades 8-10.

Math Problem Statement

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

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