IDNLearn.com provides a user-friendly platform for finding and sharing accurate answers. Get prompt and accurate answers to your questions from our community of knowledgeable experts.
Sagot :
Certainly! Let's graph the equation [tex]\( y = \frac{3}{4}x - 6 \)[/tex] and find the intercepts and slope step-by-step.
### 1. Slope-Intercept Form
The given equation is already in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. Here,
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept (the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex])
### 2. Finding the Slope
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex]. From the equation [tex]\( y = \frac{3}{4}x - 6 \)[/tex], we can see that the slope [tex]\( m \)[/tex] is [tex]\( \frac{3}{4} \)[/tex].
### 3. Finding the Y-Intercept
The y-intercept [tex]\( b \)[/tex] is the constant term in the equation, which is -6. This means the y-intercept is at the point (0, -6).
### 4. Finding the X-Intercept
The x-intercept is the point where the graph crosses the x-axis. This happens when [tex]\( y = 0 \)[/tex].
To find the x-intercept, set [tex]\( y \)[/tex] to 0 and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = \frac{3}{4}x - 6 \][/tex]
To isolate [tex]\( x \)[/tex], add 6 to both sides:
[tex]\[ 6 = \frac{3}{4}x \][/tex]
Next, multiply both sides by the reciprocal of [tex]\( \frac{3}{4} \)[/tex], which is [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ x = 6 \times \frac{4}{3} \][/tex]
Simplifying this, we get:
[tex]\[ x = 8 \][/tex]
So, the x-intercept is at the point (8, 0).
### Conclusion
Summarizing our findings:
- Slope: [tex]\( \frac{3}{4} \)[/tex] or 0.75
- Y-Intercept: (0, -6)
- X-Intercept: (-8, 0)
With this information, you can easily graph the linear equation [tex]\( y = \frac{3}{4} x - 6 \)[/tex]. Plot the intercepts and use the slope to find another point on the line for accuracy. Then, draw a straight line through these points, and you'll have the graph of the equation.
### 1. Slope-Intercept Form
The given equation is already in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. Here,
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept (the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex])
### 2. Finding the Slope
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex]. From the equation [tex]\( y = \frac{3}{4}x - 6 \)[/tex], we can see that the slope [tex]\( m \)[/tex] is [tex]\( \frac{3}{4} \)[/tex].
### 3. Finding the Y-Intercept
The y-intercept [tex]\( b \)[/tex] is the constant term in the equation, which is -6. This means the y-intercept is at the point (0, -6).
### 4. Finding the X-Intercept
The x-intercept is the point where the graph crosses the x-axis. This happens when [tex]\( y = 0 \)[/tex].
To find the x-intercept, set [tex]\( y \)[/tex] to 0 and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = \frac{3}{4}x - 6 \][/tex]
To isolate [tex]\( x \)[/tex], add 6 to both sides:
[tex]\[ 6 = \frac{3}{4}x \][/tex]
Next, multiply both sides by the reciprocal of [tex]\( \frac{3}{4} \)[/tex], which is [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ x = 6 \times \frac{4}{3} \][/tex]
Simplifying this, we get:
[tex]\[ x = 8 \][/tex]
So, the x-intercept is at the point (8, 0).
### Conclusion
Summarizing our findings:
- Slope: [tex]\( \frac{3}{4} \)[/tex] or 0.75
- Y-Intercept: (0, -6)
- X-Intercept: (-8, 0)
With this information, you can easily graph the linear equation [tex]\( y = \frac{3}{4} x - 6 \)[/tex]. Plot the intercepts and use the slope to find another point on the line for accuracy. Then, draw a straight line through these points, and you'll have the graph of the equation.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.