Sure! Let's go through the solution step by step.
To find the equation of a line in slope-intercept form, we use the formula:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
We are given:
- Slope ([tex]\( m \)[/tex]) [tex]\( = 5 \)[/tex]
- Y-intercept ([tex]\( b \)[/tex]) [tex]\( = -3 \)[/tex]
Plugging these values into the slope-intercept form, we get:
[tex]\[ y = 5x - 3 \][/tex]
Now, let's compare this equation with the provided choices:
A. [tex]\( y = 5x + 3 \)[/tex]
B. [tex]\( x = 3y - 5 \)[/tex]
C. [tex]\( y = -3x + 5 \)[/tex]
D. [tex]\( y = 5x - 3 \)[/tex]
The correct equation is:
D. [tex]\( y = 5x - 3 \)[/tex]
So, the correct answer is option D.
