examin the six diffent equations that follow
y=5x-4
y=-2x+3
y=3x+1
y=6x+2
y-5x=+2
y-4x+1=0
1) y = 5x - 4:
This is a linear equation in slope-intercept form. The coefficient of x is 5, which represents the slope of the line, while the constant term -4 is the y-intercept.
2) y = -2x + 3:
Similar to the previous equation, this is also a linear equation in slope-intercept form. The slope is -2, indicating a downward-sloping line, and the y-intercept is 3.
3) y = 3x + 1:
Again, this equation represents a linear relationship with a slope of 3 and a y-intercept of 1.
4) y = 6x + 2:
Just like the previous equations, this is a linear equation in slope-intercept form. The line represented has a slope of 6 and a y-intercept of 2.
5) y - 5x = 2:
This equation is in standard form, where the coefficients of x and y are written with opposite signs. To convert it to slope-intercept form, we can rearrange the equation as y = 5x + 2. The slope is positive 5, indicating an upward-sloping line, and the y-intercept is 2.
6) y - 4x + 1 = 0:
Similar to the previous equation, this one is also in standard form. Rearranging it to slope-intercept form yields y = 4x - 1, where the slope is 4 and the y-intercept is -1.
show me how to do them
Certainly! I will walk you through the process of solving each equation.
1) y = 5x - 4:
This equation is already in slope-intercept form, y = mx + b. The slope, m, is 5, and the y-intercept, b, is -4. You can plot this equation by starting at the y-intercept (-4), and then using the slope to find additional points on the line.
2) y = -2x + 3:
Similar to the previous equation, this equation is already in slope-intercept form. The slope, m, is -2, and the y-intercept, b, is 3. Starting at the y-intercept (3), you can use the slope to find other points on the line.
3) y = 3x + 1:
Again, this equation is already in slope-intercept form. The slope, m, is 3, and the y-intercept, b, is 1. Begin at the y-intercept (1) and use the slope to locate additional points on the line.
4) y = 6x + 2:
This equation is also in slope-intercept form. The slope, m, is 6, and the y-intercept, b, is 2. Begin at the y-intercept (2) and utilize the slope to identify extra points on the line.
5) y - 5x = 2:
To convert this equation to slope-intercept form, we need to rearrange it to isolate y. Adding 5x to both sides, we get y = 5x + 2. Now the equation is in slope-intercept form. The slope, m, is 5, and the y-intercept, b, is 2. Begin at the y-intercept (2) and employ the slope to find other points on the line.
6) y - 4x + 1 = 0:
Similarly, we need to rearrange this equation to isolate y. Adding 4x and subtracting 1 from both sides, we get y = 4x - 1. Now the equation is in slope-intercept form. The slope, m, is 4, and the y-intercept, b, is -1. Begin at the y-intercept (-1) and use the slope to identify additional points on the line.
Once you have the slope and y-intercept for each equation, you can plot the lines on a graph using these values as starting points and then connecting them.
just number no words
1) Equation: y = 5x - 4
Slope (m): 5
Y-intercept (b): -4
2) Equation: y = -2x + 3
Slope (m): -2
Y-intercept (b): 3
3) Equation: y = 3x + 1
Slope (m): 3
Y-intercept (b): 1
4) Equation: y = 6x + 2
Slope (m): 6
Y-intercept (b): 2
5) Equation: y - 5x = 2
Slope (m): 5
Y-intercept (b): 2
6) Equation: y - 4x + 1 = 0
Slope (m): 4
Y-intercept (b): -1
show me how to do them using numbers
I apologize for the confusion. Here's a step-by-step numerical breakdown for each equation:
1) y = 5x - 4
- To find the y-coordinate, substitute any value for x and solve for y.
For example, let's take x = 2:
y = 5(2) - 4
= 10 - 4
= 6
Therefore, one point on the line is (2, 6).
2) y = -2x + 3
- Similar to the previous equation, choose a value for x and solve for y.
Let's take x = 1:
y = -2(1) + 3
= -2 + 3
= 1
Hence, one point on the line is (1, 1).
3) y = 3x + 1
- Following the same process, substitute x with a value to find y.
Take x = 0:
y = 3(0) + 1
= 0 + 1
= 1
So one point on the line is (0, 1).
4) y = 6x + 2
- Substitute an arbitrary x value and calculate y.
Let x = -1:
y = 6(-1) + 2
= -6 + 2
= -4
As a result, one point on the line is (-1, -4).
5) y - 5x = 2
- This equation is in standard form, so let's convert it to slope-intercept form (y = mx + b).
y = 5x + 2
- Pick an x value and discover y.
Suppose x = 2:
y = 5(2) + 2
= 10 + 2
= 12
Hence, one point on the line is (2, 12).
6) y - 4x + 1 = 0
- Convert to slope-intercept form.
y = 4x - 1
- Select an x and determine y.
Take x = -2:
y = 4(-2) - 1
= -8 - 1
= -9
Thus, one point on the line is (-2, -9).
You can plot these points on a graph and connect them to draw the lines.