If a line whose x- and y- intercepts are equal does not pass through the origin, then its slope must be

A. 0
B. 1
C. -1
D. undefined
I'm thinking it's 0, I don't know though.

make a sketch of a line with equal intercepts,

e.g. (a,0) and (0,a)

slope = (a-0)/(0-a) = -1

To determine the slope of a line, we need to use the formula:

slope = (change in y-coordinate) / (change in x-coordinate)

Given that the line's x- and y-intercepts are equal, we can write the equation of the line in slope-intercept form as:

y = mx + b

where "m" is the slope and "b" is the y-intercept.

Since the line does not pass through the origin, the y-intercept is not 0. Therefore, the y-intercept is represented as "b" in the equation.

To determine the slope, consider that the x-intercept is equal to the y-intercept. This means that when y = 0, x will also be 0.

Plugging these values into the equation, we have:

0 = m * 0 + b

0 = b

Since the y-intercept is 0, the line passes through the origin. However, the question states that the line does not pass through the origin. Hence, the statement that the x- and y-intercepts are equal is not possible without the line passing through the origin.

Therefore, the correct answer is D. undefined.

To determine the slope of a line, you need two points on the line. In this case, we know that the line has equal x- and y-intercepts. Let's denote these intercepts as (a, 0) and (0, a), where a represents a constant.

The equation of the line passing through these two points can be found using the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

Substituting the points (a, 0) and (0, a) into the equation, we get:
0 = ma + b
a = m(0) + b

Since the x- and y-intercepts are equal, we can equate the values of a:
a = 0

Substituting this back into the previous equations, we get:
0 = m(0) + b
0 = b

So, the y-intercept is also 0.

Therefore, the equation of the line passing through the equal x- and y-intercepts is y = mx, where the slope m is yet to be determined.

Now, let's consider the fact that the line does not pass through the origin. That means the point (0, 0) is not on the line. If we substitute x = 0 and y = 0 into the equation y = mx, we get:
0 = m(0)
0 = 0

This shows that when x = 0, y is also equal to 0. Thus, the line passes through the origin, contradicting the given information.

Therefore, there is no line that satisfies the given conditions. As a result, the slope is undefined (option D), rather than 0.