Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Sure, let's graph the line with slope [tex]\( -\frac{1}{3} \)[/tex] passing through the point [tex]\( (5, 4) \)[/tex]. Here is a step-by-step solution for how to do this:
1. Identify the Point-Slope Formula:
The point-slope formula of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
2. Substitute the Given Values:
We know the slope [tex]\( m = -\frac{1}{3} \)[/tex], and the point [tex]\( (x_1, y_1) = (5, 4) \)[/tex]. Substituting these values into the equation, we get:
[tex]\[ y - 4 = -\frac{1}{3}(x - 5) \][/tex]
3. Simplify the Equation:
Distribute [tex]\( -\frac{1}{3} \)[/tex] on the right-hand side:
[tex]\[ y - 4 = -\frac{1}{3}x + \frac{5}{3} \][/tex]
Add 4 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{1}{3}x + \frac{5}{3} + 4 \][/tex]
Convert 4 to a fraction with a common denominator:
[tex]\[ y = -\frac{1}{3}x + \frac{5}{3} + \frac{12}{3} \][/tex]
Combine the fractions:
[tex]\[ y = -\frac{1}{3}x + \frac{17}{3} \][/tex]
4. Plot the Line:
- Start by plotting the point [tex]\( (5, 4) \)[/tex] on the graph.
- Use the slope to find other points. Since the slope is [tex]\( -\frac{1}{3} \)[/tex], this means that for every 3 units you move horizontally to the right, you move 1 unit vertically downwards.
Let's find another point using the slope:
- From [tex]\( (5, 4) \)[/tex], move 3 units to the right to [tex]\( x = 8 \)[/tex].
- Move 1 unit down to [tex]\( y = 3 \)[/tex].
- So, another point on the line is [tex]\( (8, 3) \)[/tex].
5. Draw the Line:
- Plot the point [tex]\( (8, 3) \)[/tex] on the graph.
- Draw a straight line passing through the two points [tex]\( (5, 4) \)[/tex] and [tex]\( (8, 3) \)[/tex].
6. Label the Graph:
- Mark the points [tex]\( (5, 4) \)[/tex] and [tex]\( (8, 3) \)[/tex] clearly.
- Write the equation of the line [tex]\( y = -\frac{1}{3}x + \frac{17}{3} \)[/tex] on the graph.
- Optionally, draw and label the x and y-axes accurately.
By following these steps, you should have a properly graph of the line passing through the point [tex]\( (5, 4) \)[/tex] with a slope of [tex]\( -\frac{1}{3} \)[/tex].
1. Identify the Point-Slope Formula:
The point-slope formula of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
2. Substitute the Given Values:
We know the slope [tex]\( m = -\frac{1}{3} \)[/tex], and the point [tex]\( (x_1, y_1) = (5, 4) \)[/tex]. Substituting these values into the equation, we get:
[tex]\[ y - 4 = -\frac{1}{3}(x - 5) \][/tex]
3. Simplify the Equation:
Distribute [tex]\( -\frac{1}{3} \)[/tex] on the right-hand side:
[tex]\[ y - 4 = -\frac{1}{3}x + \frac{5}{3} \][/tex]
Add 4 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{1}{3}x + \frac{5}{3} + 4 \][/tex]
Convert 4 to a fraction with a common denominator:
[tex]\[ y = -\frac{1}{3}x + \frac{5}{3} + \frac{12}{3} \][/tex]
Combine the fractions:
[tex]\[ y = -\frac{1}{3}x + \frac{17}{3} \][/tex]
4. Plot the Line:
- Start by plotting the point [tex]\( (5, 4) \)[/tex] on the graph.
- Use the slope to find other points. Since the slope is [tex]\( -\frac{1}{3} \)[/tex], this means that for every 3 units you move horizontally to the right, you move 1 unit vertically downwards.
Let's find another point using the slope:
- From [tex]\( (5, 4) \)[/tex], move 3 units to the right to [tex]\( x = 8 \)[/tex].
- Move 1 unit down to [tex]\( y = 3 \)[/tex].
- So, another point on the line is [tex]\( (8, 3) \)[/tex].
5. Draw the Line:
- Plot the point [tex]\( (8, 3) \)[/tex] on the graph.
- Draw a straight line passing through the two points [tex]\( (5, 4) \)[/tex] and [tex]\( (8, 3) \)[/tex].
6. Label the Graph:
- Mark the points [tex]\( (5, 4) \)[/tex] and [tex]\( (8, 3) \)[/tex] clearly.
- Write the equation of the line [tex]\( y = -\frac{1}{3}x + \frac{17}{3} \)[/tex] on the graph.
- Optionally, draw and label the x and y-axes accurately.
By following these steps, you should have a properly graph of the line passing through the point [tex]\( (5, 4) \)[/tex] with a slope of [tex]\( -\frac{1}{3} \)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
