Answer:
The value of [tex]b[/tex] is 2.
Step-by-step explanation:
The standard form of the equation of the line is of the form:
[tex]y = m\cdot x + k[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Independent and dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]k[/tex] - y-intercept, dimensionless.
Given that line [tex]l[/tex] is perpendicular to [tex]y = -\frac{2}{3}\cdot y[/tex], the slope is equal to:
[tex]m = -\frac{1}{m_{\perp}}[/tex]
Where [tex]m_{\perp}[/tex] is the slope of the perpendicular line, dimensionless.
If [tex]m_{\perp} = -\frac{2}{3}[/tex], then:
[tex]m = -\frac{1}{\left(-\frac{2}{3}\right) }[/tex]
[tex]m = \frac{3}{2}[/tex]
If [tex]x = 0[/tex] and [tex]y = -13[/tex], the y-intercept of the line [tex]l[/tex] is:
[tex]-13 = \frac{3}{2}\cdot (0) +k[/tex]
[tex]k = -13[/tex]
The equation of the line [tex]l[/tex] is [tex]y = \frac{3}{2}\cdot x -13[/tex]. Given that [tex]y = b[/tex] and [tex]x = 10[/tex], the value of [tex]b[/tex] is:
[tex]b = \frac{3}{2}\cdot (10)-13[/tex]
[tex]b = 15-13[/tex]
[tex]b = 2[/tex]
The value of [tex]b[/tex] is 2.
