At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

What is the equation of the line that passes through the point [tex]\((-5, 4)\)[/tex] and has a slope of 0?

Sagot :

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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.