Understanding Linear Equations | Exploring Slope and Y-Intercept in Mathematics

y = -x – 1

The equation you have given is a linear equation in the form of y = mx + c, where m is the slope of the line and c is the y-intercept

The equation you have given is a linear equation in the form of y = mx + c, where m is the slope of the line and c is the y-intercept. Let’s break it down:

Slope (m): In this equation, the coefficient of x is -1, which means the slope of the line is -1. A negative slope indicates that the line is decreasing as you move from left to right.

Y-intercept (c): The y-intercept is the point on the y-axis where the line intersects. In this equation, the constant term is -1, so the y-intercept is -1.

Graphically, this equation represents a straight line that slopes downwards and intersects the y-axis at the point (0, -1). As you move one unit to the right (positive x), the line decreases by one unit (negative y). Similarly, as you move one unit to the left (negative x), the line increases by one unit (positive y).

Furthermore, you can use this equation to find the value of y for a given value of x, or vice versa. For example, if you are asked to find the value of y when x is 2, you can substitute x = 2 into the equation:
y = -(2) – 1
y = -2 – 1
y = -3
So, when x = 2, y is equal to -3.

Conversely, if you are given a value of y and asked to find the corresponding value of x, you can rearrange the equation and solve for x. For example, if y = -5, you can substitute y = -5 into the equation and solve for x:
-5 = -x – 1
Add 1 to both sides:
-4 = -x
Multiply by -1 (or divide by -1) to isolate x:
x = 4

Therefore, when y = -5, x is equal to 4.

This is a brief explanation of the given equation and its interpretation. If you have any more specific questions or need further clarification, feel free to ask.

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