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Which of the following is the equation of a line in slope-intercept form for a line with slope [tex]\(5\)[/tex] and [tex]\(y\)[/tex]-intercept at [tex]\((0, -3)\)[/tex]?

A. [tex]\(y = 5x + 3\)[/tex]
B. [tex]\(x = 3y - 5\)[/tex]
C. [tex]\(y = -3x + 5\)[/tex]
D. [tex]\(y = 5x - 3\)[/tex]

Sagot :

GinnyAnsweridn
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.
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