Question

Slope -intercept form

Answer 1

[AI-generated answer — Bot GPT 3.5]

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept of the line.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The slope-intercept form of a linear equation is given by:

y = mx + b

Where:
- "y" represents the dependent variable (usually the output or the "dependent" variable).
- "x" represents the independent variable (usually the input or the "independent" variable).
- "m" represents the slope of the line.
- "b" represents the y-intercept, which is the y-coordinate where the line intersects the y-axis.

In this form, the equation represents a line on a graph, with "m" representing the slope (or steepness) of the line, and "b" representing the y-coordinate of the point where the line intersects the y-axis.

By using the slope and the y-intercept, you can easily plot the line on a graph or find the values of y for a given x or vice versa.

Answer 3

[AI-generated answer — Explain Bot]

The slope-intercept form of a linear equation is represented as y = mx + b, where "m" is the slope of the line and "b" is the y-intercept of the line.

To understand how to find the slope-intercept form of a linear equation, you need two pieces of information: the slope of the line, which represents how steep the line is, and the y-intercept, which represents the point where the line crosses the y-axis.

Let's break down the equation:

- The letter "y" represents the dependent variable or the value of the vertical coordinate.
- The letter "x" represents the independent variable or the value of the horizontal coordinate.
- The letter "m" represents the slope, which determines the rate of change of the line.
- The letter "b" represents the y-intercept, which indicates where the line intersects the y-axis.

To find the slope-intercept form of a linear equation, you can follow these steps:

1. Determine the slope of the line:
- If you have two points on the line, you can use the slope formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
- If you are given the slope directly, you can use that value for "m."

2. Determine the y-intercept of the line:
- If you have the y-intercept value, you can directly use that value for "b."
- If you don't have the y-intercept, you can substitute the values of one of the given points and the slope into the equation y = mx + b, and solve for "b."

3. Once you have the values for "m" and "b," plug them into the slope-intercept form equation y = mx + b to get the equation of the line.

Remember that the slope-intercept form is just one way to represent a linear equation. There are other forms, such as the point-slope form or the standard form, depending on what information you have available.