Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To work out the gradient of each line, let's follow a step-by-step process for each equation.
### Finding the Gradient of the Line [tex]\( y = 5x - 3 \)[/tex]
1. Identify the form of the equation:
- The given equation is [tex]\( y = 5x - 3 \)[/tex].
- This is in the slope-intercept form, [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the gradient.
2. Determine the gradient:
- By comparing [tex]\( y = 5x - 3 \)[/tex] to [tex]\( y = mx + c \)[/tex], we see that [tex]\( m = 5 \)[/tex].
Therefore, the gradient of the line [tex]\( y = 5x - 3 \)[/tex] is [tex]\( 5 \)[/tex].
### Finding the Gradient of the Line [tex]\( 3y - 12x + 7 = 0 \)[/tex]
1. Rearrange the equation into the slope-intercept form:
- Start with [tex]\( 3y - 12x + 7 = 0 \)[/tex].
- Add [tex]\( 12x \)[/tex] to both sides: [tex]\( 3y = 12x - 7 \)[/tex].
- Divide by 3: [tex]\( y = 4x - \frac{7}{3} \)[/tex].
2. Identify the gradient:
- The equation is now in the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the gradient.
- Here, [tex]\( m = 4 \)[/tex].
Therefore, the gradient of the line [tex]\( 3y - 12x + 7 = 0 \)[/tex] is [tex]\( 4 \)[/tex].
Summarizing the gradients:
- The gradient of the line [tex]\( y = 5x - 3 \)[/tex] is [tex]\( 5 \)[/tex].
- The gradient of the line [tex]\( 3y - 12x + 7 = 0 \)[/tex] is [tex]\( 4 \)[/tex].
### Finding the Gradient of the Line [tex]\( y = 5x - 3 \)[/tex]
1. Identify the form of the equation:
- The given equation is [tex]\( y = 5x - 3 \)[/tex].
- This is in the slope-intercept form, [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the gradient.
2. Determine the gradient:
- By comparing [tex]\( y = 5x - 3 \)[/tex] to [tex]\( y = mx + c \)[/tex], we see that [tex]\( m = 5 \)[/tex].
Therefore, the gradient of the line [tex]\( y = 5x - 3 \)[/tex] is [tex]\( 5 \)[/tex].
### Finding the Gradient of the Line [tex]\( 3y - 12x + 7 = 0 \)[/tex]
1. Rearrange the equation into the slope-intercept form:
- Start with [tex]\( 3y - 12x + 7 = 0 \)[/tex].
- Add [tex]\( 12x \)[/tex] to both sides: [tex]\( 3y = 12x - 7 \)[/tex].
- Divide by 3: [tex]\( y = 4x - \frac{7}{3} \)[/tex].
2. Identify the gradient:
- The equation is now in the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the gradient.
- Here, [tex]\( m = 4 \)[/tex].
Therefore, the gradient of the line [tex]\( 3y - 12x + 7 = 0 \)[/tex] is [tex]\( 4 \)[/tex].
Summarizing the gradients:
- The gradient of the line [tex]\( y = 5x - 3 \)[/tex] is [tex]\( 5 \)[/tex].
- The gradient of the line [tex]\( 3y - 12x + 7 = 0 \)[/tex] is [tex]\( 4 \)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.