First, you'll need a linear model with Height and Gender interaction. Try:
Fit <- lm(formula = Velocity ~ Height * Gender, data = PlotData_df)
Then choose whether or not to show the fitted regression function / equation. You'll need two equations, one for males and the other for females. Because we choose to plug in coefficients / numbers, there is no alternative option. The instructions below will show you how to obtain them.
## formatted coefficients
theta <- signif(fit$coef, digits = 2)
# (Intercept) Height GenderMale Height:GenderMale
# 4.42 -0.30 -1.01 0.54
## equation for Female:
eqn_Female <- paste0("Velocity = ", theta[2], " * Height + ", theta[1])
# [1] "Velocity = -0.30 * Height + 4.42"
## equation for Male:
eqn_Male <- paste0("Velocity = ", theta[2] + theta[4], " * Height + ", theta[1] + theta[3])
# [1] "Velocity = 0.24 * Height + 3.41"
The slope for Male is theta[2] + theta[4], while the intercept is theta[1] + theta[3]. You can familiarize yourself with ANOVA and contrast treatment for factor variables.