To determine the equation of the line in the form [tex]\( y = mx + b \)[/tex] given specific intercepts, let's identify the components [tex]\( m \)[/tex] (the slope) and [tex]\( b \)[/tex] (the y-intercept).
1. Identify the y-intercept ([tex]\( b \)[/tex]):
- The y-intercept is the point where the line crosses the y-axis. By definition, this is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
- Given that the y-intercept is -4, we directly get:
[tex]\[
b = -4
\][/tex]
2. Determine the slope ([tex]\( m \)[/tex]):
- The slope of a line indicates the change in [tex]\( y \)[/tex] for a unit change in [tex]\( x \)[/tex].
- Given two points on the line: the x-intercept (5, 0) and the y-intercept (0, -4), we can calculate the slope using the slope formula:
[tex]\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- For the points (5, 0) and (0, -4):
[tex]\[
m = \frac{0 - (-4)}{5 - 0} = \frac{4}{5} = 0.8
\][/tex]
Thus, the numbers are:
- The number [tex]\( m \)[/tex] (the slope) is 0.8.
- The number [tex]\( b \)[/tex] (the y-intercept) is -4.
