Answered

IDNLearn.com provides a seamless experience for finding and sharing answers. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.

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 greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.