geometry help, please explain when answered

Question

What is the slope of a line that is parallel to the following: y=10x+1 

Answer 1

Sure! Here’s a detailed Explanation:

The Equation of a Line in Slope-Intercept Form is y = mx + b

In this equation:

1. (m) signifies the slope of the line.
2. (b) indicates the y-intercept, which is the point at which the line intersects the y-axis.

In the equation you mentioned: y = 10x + 1

This formula is already in slope-intercept format, where:

1. The coefficient of (x) (which is 10) represents the slope (m).
2. The constant term (which is 1) denotes the y-intercept (b).

Thus, the slope (m) for this line is: m = 10

Parallel lines are those that never meet. They maintain a consistent distance from each other, regardless of how far they stretch. A significant characteristic of parallel lines is that they share the same slope.

This means that if two lines are parallel, their slopes will be equal.

Since you need to find the slope of a line parallel to the given line (y = 10x + 1), and knowing that the slope of this line is 10, any line that is parallel to it will also have a slope of 10.

Thus, the slope of the parallel line is: m = 10

Answer 2

Hi Kaley, when finding the slope of a line, there is a theorem called slope-intercept form which can help understand what the slope is. The equation is y=mx+b where:

y - the y coordinate

m - the slope

x - the x coordinate

b - the y-intercept of the line (where the value of y passes on the y-axis)

So, knowing the above, we can take your equation of y = 10x+1 as below broken down:

y - the y coordinate

m - 10

x - the x coordinate

b - 1

So what this says is any function of y that has a slope (m) of 10 would be parallel to y=10x + 1. So, we can have for example, y = 10x + 5, y = 10x - 2, or even y = 10x (in this example, b is 0 so we don't see the value, but remember there is ALWAYS a value for b)

Answer 3

Hi Kaley

10

Parallel lines have the same slope.

Your line is in Slope Intercept Form y = mx + b, where m is the slope

y = 10x + 1

In the line above m = 10.

So a parallel will have exactly the same slope as the given line y = 10x + 1.

Answer 4

The slope of the line is always going to be y=mx+b with m representing the slope. Any parallel line on the graph is going to have the same slope, so for example, if the slope of the line with equation y = 4x+5 is 4, then any line parallel to it has the same slope 4. Hope this helps you to your answer!