To determine the slope of a line with a given y-intercept and x-intercept, we follow a systematic approach:
1. Define the intercepts: The y-intercept is the point where the line crosses the y-axis, and it is given as -1. This can be written as the point (0, -1). The x-intercept is the point where the line crosses the x-axis, and it is given as 4. This can be written as the point (4, 0).
2. Understand the concept of the slope: The slope of a line (often denoted as [tex]\( m \)[/tex]) is a measure of how steep the line is. It is calculated as the change in the y-coordinates (vertical change) divided by the change in the x-coordinates (horizontal change) between any two points on the line.
3. Formula for slope: The slope [tex]\( m \)[/tex] can be calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are two points on the line.
4. Identify the points: In this case, we have:
- Point 1: [tex]\( (0, -1) \)[/tex] (y-intercept)
- Point 2: [tex]\( (4, 0) \)[/tex] (x-intercept)
5. Plug the points into the formula:
[tex]\[
m = \frac{0 - (-1)}{4 - 0}
\][/tex]
6. Simplify the numerator and the denominator:
- The numerator [tex]\( 0 - (-1) \)[/tex] is equal to [tex]\( 0 + 1 = 1 \)[/tex]
- The denominator [tex]\( 4 - 0 \)[/tex] is equal to [tex]\( 4 \)[/tex]
7. Calculate the slope:
[tex]\[
m = \frac{1}{4} = 0.25
\][/tex]
Thus, the slope of the line with a y-intercept of -1 and an x-intercept of 4 is [tex]\( 0.25 \)[/tex].
