To find the equation of the line parallel to a given line with an [tex]$x$[/tex]-intercept of 4, follow these steps:
1. Identify the Slope of the Given Line:
- The slope-intercept form of a line is given by [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- Since the given line equation is not specified, we'll assume a line with a slope of [tex]\(m = 1\)[/tex]. (Note: Replace this slope with the actual slope if provided.)
2. Recognize Key Characteristic of Parallel Lines:
- Parallel lines have the same slope. This means the slope of the new line will also be [tex]\(m = 1\)[/tex].
3. Use the Given x-intercept to Determine the New Line’s Equation:
- The x-intercept of a line is the point where the line crosses the x-axis. At this point, [tex]\(y = 0\)[/tex].
- For an x-intercept of 4, the coordinate at this point is [tex]\((4, 0)\)[/tex].
4. Formulate the Equation with the x-intercept:
- Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 0\)[/tex] into the slope-intercept form. We have [tex]\(y = mx + b \Rightarrow 0 = 1 \cdot 4 + b\)[/tex].
- Solve for [tex]\(b\)[/tex]:
[tex]\[
0 = 4 + b \Rightarrow b = -4
\][/tex]
5. Write the Final Equation:
- With [tex]\(m = 1\)[/tex] and [tex]\(b = -4\)[/tex], the equation of the line in slope-intercept form is:
[tex]\[
y = 1x - 4 \Rightarrow y = x - 4
\][/tex]
Therefore, the equation of the line parallel to the given line with an [tex]\(x\)[/tex]-intercept of 4 is:
[tex]\[
y = 1 \cdot x - 4 \Rightarrow y = x - 4
\][/tex]
