Answered

IDNLearn.com offers a user-friendly platform for finding and sharing knowledge. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

What is the point-slope equation of a line with slope [tex]\(-4\)[/tex] that contains the point [tex]\((-2, 7)\)[/tex]?

A. [tex]\[ y + 7 = -4(x + 2) \][/tex]

B. [tex]\[ y - 7 = -4(x - 2) \][/tex]

C. [tex]\[ y - 7 = -4(x + 2) \][/tex]

D. [tex]\[ y + 7 = -4(x - 2) \][/tex]

Sagot :

GinnyAnsweridn
To find the point-slope equation of a line with a given slope that passes through a specific point, we use the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\( m \)[/tex] is the slope of the line and [tex]\( (x_1, y_1) \)[/tex] is the given point on the line.

Given:
- The slope [tex]\( m = -4 \)[/tex]
- The point [tex]\( (x_1, y_1) = (-2, 7) \)[/tex]

Substitute the given slope and point into the point-slope form equation:

[tex]\[ y - 7 = -4(x - (-2)) \][/tex]

Simplify the expression inside the parentheses:

[tex]\[ y - 7 = -4(x + 2) \][/tex]

Thus, the correct point-slope equation for the line is:

[tex]\[ y - 7 = -4(x + 2) \][/tex]

Looking at the given options:
A. [tex]\( y + 7 = -4(x + 2) \)[/tex]
B. [tex]\( y - 7 = -4(x - 2) \)[/tex]
C. [tex]\( y - 7 = -4(x + 2) \)[/tex]
D. [tex]\( y + 7 = -4(x - 2) \)[/tex]

The correct option is:
C. [tex]\( y - 7 = -4(x + 2) \)[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.