Logistic regression with two slopes and one intercept I am using R to fit a logistic model to some data. The problem is as follows:
"The effects of the dose of poison $(x)$, in milligrammes, and the method of delivery $(w)$ on the
probability of survival were examined in a study of rats. The two methods of delivery were
as a solid with food or as a liquid in water. For each combination of dose and method of
delivery, a certain number of rats $(r)$ were used and the number who survived $(y)$ is recorded.
Below are the data.

Now when I plot these data, it looks like a model that has a different slope for each delivery method but the same intercept would be suitable:

How would I tell R to do this? I know that to fit a model with different intercepts but the same slope is "glm(p~x+w,...)" and to fit a model with two slopes and two intercepts is "glm(p~x+w+x:w,...)" but can't figure out the case for different slopes and the same intercept.

In order to have separate slopes for each group but equal intercepts, explicitly require that in the model.
Instead of
$$
\beta_0+\beta_1x_{group}+\beta_2x_{dose}+\beta_3x_{group}x_{dose}+\epsilon
$$
try
$$
\beta_0+\beta_1x_{dose}+\beta_2x_{dose}+\epsilon
$$
The R code would be something like glm(y~dose + dose:group, family = binomial). This takes the interaction between the dose and the group (to achieve multiple slopes) while excluding the interaction between the intercept and the two groups that you would get by regressing on the group variable on its own.
