Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Mr. Shaw graphs the function [tex]$f(x) = -5x + 2$[/tex] for his class. The line contains the point [tex]$(-2, 12)$[/tex]. What is the point-slope form of the equation of the line he graphed?

A. [tex]$y - 12 = -5(x + 2)$[/tex]
B. [tex][tex]$y - 12 = 2(x + 2)$[/tex][/tex]
C. [tex]$y + 12 = 2(x - 2)$[/tex]
D. [tex]$y + 12 = -5(x - 2)$[/tex]

Sagot :

GinnyAnswer
To find the point-slope form of the equation for the line that Mr. Shaw has graphed, we need to use the point-slope formula for a line. The point-slope form of a line is given by the equation:

[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 of the line.

Given the function [tex]\( f(x) = -5x + 2 \)[/tex]:

1. Identify the slope [tex]\(m\)[/tex]: The slope [tex]\(m\)[/tex] is the coefficient of [tex]\(x\)[/tex] in the linear equation. Here, the function is in the form [tex]\( y = -5x + 2 \)[/tex], so the slope [tex]\( m = -5 \)[/tex].

2. Identify a point [tex]\((x_1, y_1)\)[/tex] on the line: We are given that the point [tex]\((-2, 12)\)[/tex] lies on the line.

Next, we substitute the slope [tex]\(m = -5\)[/tex] and the point [tex]\((x_1, y_1) = (-2, 12)\)[/tex] into the point-slope form equation:

[tex]\[ y - 12 = -5(x - (-2)) \][/tex]

Simplify the expression inside the parentheses:

[tex]\[ y - 12 = -5(x + 2) \][/tex]

Therefore, the point-slope form of the equation for the line Mr. Shaw has graphed is:

[tex]\[ y - 12 = -5(x + 2) \][/tex]

The correct option is:

[tex]\[ \boxed{y - 12 = -5(x + 2)} \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.