diff --git a/src/aff_expr.jl b/src/aff_expr.jl
index 69c230fb927..9377d16bc63 100644
--- a/src/aff_expr.jl
+++ b/src/aff_expr.jl
@@ -837,7 +837,16 @@ expressions. To make common operations like `lower_bound(x)` work, we should
 forward the method if and only if `x` is convertible to a `GenericVariableRef`.
 """
 function _eval_as_variable(f::F, x::GenericAffExpr, args...) where {F}
-    if length(x.terms) != 1
+    if !iszero(x.constant)
+        error(
+            """
+            Cannot call `$f` with the affine expression `$x` because the expression \
+            has a non-zero constant.
+
+            `$f` can be called only with affine expressions of the form `1.0 * x`.
+            """,
+        )
+    elseif length(x.terms) != 1
         error(
             """
             Cannot call `$f` with the affine expression `$x` because the expression
diff --git a/test/test_expr.jl b/test/test_expr.jl
index b86230924b8..921f73ecf50 100644
--- a/test/test_expr.jl
+++ b/test/test_expr.jl
@@ -507,6 +507,10 @@ function test_aff_expr_complex_HermitianPSDCone()
         ),
         start_value(imag(x[2, 1])),
     )
+    return
+end
+
+function test_eval_as_variable_no_terms()
     y = AffExpr(0.0)
     @test_throws(
         ErrorException(
@@ -522,6 +526,24 @@ function test_aff_expr_complex_HermitianPSDCone()
     return
 end
 
+function test_eval_as_variable_with_constant()
+    model = Model()
+    @variable(model, x, start = 1)
+    y = 1.0 * x + 2.0
+    @test_throws(
+        ErrorException(
+            """
+            Cannot call `$start_value` with the affine expression `$y` because \
+            the expression has a non-zero constant.
+
+            `$start_value` can be called only with affine expressions of the form `1.0 * x`.
+            """,
+        ),
+        start_value(y),
+    )
+    return
+end
+
 function test_multiply_expr_MA_Zero()
     model = Model()
     @variable(model, x)