If the y intercept of a graph of x+y=1 is changed to -1 and the x intercept remains the same, what is the equation of the new graph?

y = -x + 1 is your origonal equation with y-intercept at y=1. The x intercept is at x = 1

You want an equation for which y = mx -1, and with x-intercept of 1. So require that x=1 when y = 0

y = x-1 is your equation

To find the equation of the new graph, we need to understand the relationship between the intercepts and the equation of a straight line.

The y-intercept is the point where the line intersects the y-axis, denoted as (0, y). The x-intercept is the point where the line intersects the x-axis, denoted as (x, 0).

Let's start with the original equation x + y = 1. To find the y-intercept, we set x = 0 and solve for y. Substituting x = 0 into the equation gives us 0 + y = 1, which simplifies to y = 1. Therefore, the original y-intercept is (0, 1).

Now, let's consider the new scenario where the y-intercept is changed to -1. The new y-intercept is now (0, -1).

The x-intercept remains the same, which means it is (x, 0).

We know that the equation of a straight line can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept.

To find the equation of the new graph, we first need to determine the slope (m). We can calculate the slope using two points, namely the original y-intercept (0, 1) and the new y-intercept (0, -1). The formula for slope (m) is:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the two points, we have:

m = (-1 - 1) / (0 - 0) = -2 / 0

Since division by zero is undefined, the slope (m) is undefined. This means that the line is vertical.

For a vertical line with an undefined slope, the equation is of the form x = a, where 'a' is the x-coordinate of any point on the line.

Since the x-intercept remains the same, we can determine the value of 'a' by substituting the x-coordinate of the x-intercept into the equation. Thus, the new equation of the graph is x = (value of x-intercept).

In conclusion, if the y-intercept of x + y = 1 is changed to -1 while the x-intercept remains the same, the equation of the new graph is x = (value of x-intercept).