To determine the correct equation of a line in slope-intercept form, we need to use the formula [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
We are given the following values:
- The y-intercept ([tex]\( b \)[/tex]) is -5
- The slope ([tex]\( m \)[/tex]) is 2
Substituting these values into the slope-intercept formula, we get:
[tex]\[
y = 2x - 5
\][/tex]
Now, let's compare this with the given options:
A. [tex]\( x = 2x + 5 \)[/tex] - This is not in the correct form.
B. [tex]\( y = 2x - 5 \)[/tex] - This equation matches our derived equation.
C. [tex]\( y = 5x - 2 \)[/tex] - This has the slope and y-intercept reversed.
D. [tex]\( y = -5x + 2 \)[/tex] - This has the incorrect slope and y-intercept.
The correct choice is:
[tex]\[
\boxed{y = 2x - 5}
\][/tex]
So the answer is:
B. [tex]\( y = 2x - 5 \)[/tex]
