Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine the slope of the line given by the equation [tex]\( 5x - 4y = 24 \)[/tex], we need to convert this equation into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Here's a step-by-step process:
1. Start with the given equation:
[tex]\[ 5x - 4y = 24 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation. First, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -4y = -5x + 24 \][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing each term by [tex]\(-4\)[/tex]:
[tex]\[ y = \frac{-5x + 24}{-4} \][/tex]
4. Simplify the equation by distributing the division:
[tex]\[ y = \frac{-5}{-4}x + \frac{24}{-4} \][/tex]
5. Simplify the fractions:
[tex]\[ y = \frac{5}{4}x - 6 \][/tex]
The equation is now in slope-intercept form [tex]\( y = mx + b \)[/tex]. From this form, we can identify the slope [tex]\( m \)[/tex].
The slope [tex]\( m \)[/tex] is:
[tex]\[ \frac{5}{4} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{5}{4}} \][/tex]
Here's a step-by-step process:
1. Start with the given equation:
[tex]\[ 5x - 4y = 24 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation. First, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -4y = -5x + 24 \][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing each term by [tex]\(-4\)[/tex]:
[tex]\[ y = \frac{-5x + 24}{-4} \][/tex]
4. Simplify the equation by distributing the division:
[tex]\[ y = \frac{-5}{-4}x + \frac{24}{-4} \][/tex]
5. Simplify the fractions:
[tex]\[ y = \frac{5}{4}x - 6 \][/tex]
The equation is now in slope-intercept form [tex]\( y = mx + b \)[/tex]. From this form, we can identify the slope [tex]\( m \)[/tex].
The slope [tex]\( m \)[/tex] is:
[tex]\[ \frac{5}{4} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{5}{4}} \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.