Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To graph the equation [tex]\( y + 6 = \frac{4}{5}(x + 3) \)[/tex], we will transform it into the slope-intercept form [tex]\( y = mx + b \)[/tex] and identify its slope and y-intercept.
1. Start with the given equation:
[tex]\[ y + 6 = \frac{4}{5}(x + 3) \][/tex]
2. Distribute the fraction on the right-hand side:
[tex]\[ y + 6 = \frac{4}{5}x + \frac{4}{5} \times 3 \][/tex]
[tex]\[ y + 6 = \frac{4}{5}x + \frac{12}{5} \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 6 from both sides:
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - 6 \][/tex]
4. Convert 6 into a fraction with a denominator of 5 to combine the fractions:
[tex]\[ 6 = \frac{30}{5} \][/tex]
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - \frac{30}{5} \][/tex]
5. Combine the terms:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
Here:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{4}{5} \)[/tex] or 0.8
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -\frac{18}{5} \)[/tex] or -3.6
Next, we need two points to graph the line:
- The y-intercept itself is a point: [tex]\((0, -3.6)\)[/tex]
Let's choose another point by selecting [tex]\( x = 5 \)[/tex]:
\- Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = \frac{4}{5}(5) - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - 3.6 \][/tex]
[tex]\[ y = 0.4 \][/tex]
So, the coordinates of the second point are [tex]\((5, 0.4)\)[/tex].
In conclusion:
- The slope is 0.8.
- The y-intercept is -3.6.
- Two points on the line are [tex]\((0, -3.6)\)[/tex] and [tex]\((5, 0.4)\)[/tex].
You can now use these points to graph the line. Select the line tool and plot the points:
1. Start at [tex]\((0, -3.6)\)[/tex]
2. Move to [tex]\((5, 0.4)\)[/tex]
Draw the line through these points to graph the equation.
1. Start with the given equation:
[tex]\[ y + 6 = \frac{4}{5}(x + 3) \][/tex]
2. Distribute the fraction on the right-hand side:
[tex]\[ y + 6 = \frac{4}{5}x + \frac{4}{5} \times 3 \][/tex]
[tex]\[ y + 6 = \frac{4}{5}x + \frac{12}{5} \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 6 from both sides:
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - 6 \][/tex]
4. Convert 6 into a fraction with a denominator of 5 to combine the fractions:
[tex]\[ 6 = \frac{30}{5} \][/tex]
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - \frac{30}{5} \][/tex]
5. Combine the terms:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
Here:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{4}{5} \)[/tex] or 0.8
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -\frac{18}{5} \)[/tex] or -3.6
Next, we need two points to graph the line:
- The y-intercept itself is a point: [tex]\((0, -3.6)\)[/tex]
Let's choose another point by selecting [tex]\( x = 5 \)[/tex]:
\- Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = \frac{4}{5}(5) - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - 3.6 \][/tex]
[tex]\[ y = 0.4 \][/tex]
So, the coordinates of the second point are [tex]\((5, 0.4)\)[/tex].
In conclusion:
- The slope is 0.8.
- The y-intercept is -3.6.
- Two points on the line are [tex]\((0, -3.6)\)[/tex] and [tex]\((5, 0.4)\)[/tex].
You can now use these points to graph the line. Select the line tool and plot the points:
1. Start at [tex]\((0, -3.6)\)[/tex]
2. Move to [tex]\((5, 0.4)\)[/tex]
Draw the line through these points to graph the equation.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.