Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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

Sagot :

GinnyAnswer
To find the equation of a line in slope-intercept form, we start by understanding the slope-intercept form itself, which is given by:

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

Here:
- [tex]\(m\)[/tex] is the slope of the line.
- [tex]\(b\)[/tex] is the y-intercept, which is the value of [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is 0.

Given the problem:
- The slope ([tex]\(m\)[/tex]) is 5.
- The y-intercept ([tex]\(b\)[/tex]) is -3.

Substitute these values into the slope-intercept form equation:

[tex]\[ y = 5x + (-3) \][/tex]

This simplifies to:

[tex]\[ y = 5x - 3 \][/tex]

Now, let's compare this equation with the provided options:

A. [tex]\( y = 5x + 3 \)[/tex]

B. [tex]\( y = 5x - 3 \)[/tex]

C. [tex]\( x = 3y - 5 \)[/tex]

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

The correct equation from the comparison is:

[tex]\[ \boxed{y = 5x - 3} \][/tex]

Hence, the correct option is:

[tex]\[ \boxed{B} \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.