Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

What is the equation of the line that passes through the point [tex]$(2,-4)$[/tex] and has a slope of [tex]-4[/tex]?

[tex]\square[/tex]

Sagot :

GinnyAnswer
Let's find the equation of the line that passes through the point [tex]\((2, -4)\)[/tex] and has a slope of [tex]\(-4\)[/tex].

To do this, we can use the point-slope form of a line, which is given by:

[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. Given [tex]\((x_1, y_1) = (2, -4)\)[/tex] and [tex]\(m = -4\)[/tex], we can substitute these values into the point-slope form:

[tex]\[ y - (-4) = -4(x - 2) \][/tex]

Simplify the left side of the equation:

[tex]\[ y + 4 = -4(x - 2) \][/tex]

Next, we expand the right side:

[tex]\[ y + 4 = -4x + 8 \][/tex]

To get the equation into slope-intercept form [tex]\(y = mx + b\)[/tex], we need to isolate [tex]\(y\)[/tex]. Subtract 4 from both sides to achieve this:

[tex]\[ y = -4x + 8 - 4 \][/tex]

Simplify the expression on the right side:

[tex]\[ y = -4x + 4 \][/tex]

Therefore, the equation of the line that passes through the point [tex]\((2, -4)\)[/tex] and has a slope of [tex]\(-4\)[/tex] is:

[tex]\[ y = -4x + 4 \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.