To determine the equation of a line given a slope and a y-intercept, one should use the slope-intercept form of a linear equation, which is written as:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Given the slope [tex]\( \frac{5}{2} \)[/tex] and the y-intercept [tex]\( -\frac{8}{3} \)[/tex], we can directly substitute these values into the slope-intercept form as follows:
1. The slope [tex]\( m \)[/tex] is [tex]\( \frac{5}{2} \)[/tex].
2. The y-intercept [tex]\( b \)[/tex] is [tex]\( -\frac{8}{3} \)[/tex].
Substitute these values into the slope-intercept form:
[tex]\[ y = \left( \frac{5}{2} \right)x + \left( -\frac{8}{3} \right) \][/tex]
Simplify the equation for clarity:
[tex]\[ y = \frac{5}{2} x - \frac{8}{3} \][/tex]
Therefore, the equation of the line with a slope of [tex]\( \frac{5}{2} \)[/tex] and a y-intercept of [tex]\( -\frac{8}{3} \)[/tex] is:
[tex]\[ y = \frac{5}{2} x - \frac{8}{3} \][/tex]
Thus, the equation representing the line is:
[tex]\[ y = \frac{5}{2} x - \frac{8}{3} \][/tex]
