Certainly! Let's determine the equation of the line given the point and slope.
1. Identify the given information:
- The point through which the line passes: [tex]\((-5, 4)\)[/tex]
- The slope of the line, [tex]\(m\)[/tex]: [tex]\(0\)[/tex]
2. Recall the point-slope form of the equation of a line:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope.
3. Substitute the given point [tex]\((-5, 4)\)[/tex] and the slope [tex]\(m = 0\)[/tex] into the point-slope form:
[tex]\[
y - 4 = 0(x + 5)
\][/tex]
4. Simplify the equation:
Since multiplying by zero eliminates the [tex]\(x + 5\)[/tex] term:
[tex]\[
y - 4 = 0
\][/tex]
5. Solve for [tex]\(y\)[/tex]:
Adding 4 to both sides to isolate [tex]\(y\)[/tex]:
[tex]\[
y = 4
\][/tex]
So, the equation of the line that passes through the point [tex]\((-5, 4)\)[/tex] and has a slope of 0 is:
[tex]\[
y = 4
\][/tex]
This is the final equation of the line.
