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Write an equation of the line with the given slope, [tex]\( m \)[/tex], and [tex]\( y \)[/tex]-intercept [tex]\((0, b)\)[/tex].

Given:
[tex]\[ m = 7, \, b = -4 \][/tex]

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

Sagot :

GinnyAnsweridn
To write the equation of a line given the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( (0, b) \)[/tex], we use the slope-intercept form of a line, which is:

[tex]\[ y = mx + b \][/tex]

Here, [tex]\( m \)[/tex] is the slope, and [tex]\( b \)[/tex] is the y-intercept.

Given:
- Slope [tex]\( m = 7 \)[/tex]
- Y-intercept [tex]\( b = -4 \)[/tex]

Substitute these values into the slope-intercept equation:

[tex]\[ y = 7x - 4 \][/tex]

Thus, the equation of the line is [tex]\( y = 7x - 4 \)[/tex].

Looking at the choices given in the question, the correct answer is:

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

The other options available are:
A. [tex]\( y = 4x - 7 \)[/tex]
B. [tex]\( y = -7x + 4 \)[/tex]
C. [tex]\( y = -4x + 7 \)[/tex]

These do not match the derived equation of the line with the given slope and y-intercept. Therefore, option D, [tex]\( y = 7x - 4 \)[/tex], is the correct answer.
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