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Which of the following is the equation of a line in slope-intercept form for a line with slope [tex]$=4$[/tex] and [tex]$y$[/tex]-intercept at [tex]$(0,2)$[/tex]?

A. [tex]$x=-2x-4$[/tex]
B. [tex]$y=4x-2$[/tex]
C. [tex]$y=4x+2$[/tex]
D. [tex]$y=2x+4$[/tex]

Sagot :

GinnyAnsweridn
To determine the equation of a line in slope-intercept form, we use the formula:

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

where:
- [tex]\( m \)[/tex] represents the slope of the line
- [tex]\( b \)[/tex] represents the y-intercept, which is the point where the line crosses the y-axis.

Given the slope ([tex]\( m \)[/tex]) is [tex]\( 4 \)[/tex] and the y-intercept ([tex]\( b \)[/tex]) is [tex]\( 2 \)[/tex], we can substitute these values into the slope-intercept equation.

Substituting [tex]\( m = 4 \)[/tex] and [tex]\( b = 2 \)[/tex]:

[tex]\[ y = 4x + 2 \][/tex]

Now, let's match this equation with the given choices:

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

This equation is not in the correct form for a line (it should be [tex]\( y = \ldots \)[/tex]).

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

This equation has the correct slope but the incorrect y-intercept.

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

This equation has the correct slope and the correct y-intercept.

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

This equation has an incorrect slope and y-intercept.

Therefore, the correct option is:

[tex]\[ \boxed{3} \][/tex] or Option C.
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